Begin the cheesecake a day ahead. The different components may also be prepared up to a week in advance.
Preheat your oven to 350°F.
Pierce holes in the skin of the sweet potatoes to vent them while they bake. Put the potatoes onto a sheet pan and bake them for 1 hour.
An alternative, albeit inferior, method is to peel, quarter and boil the potatoes until tender. This is inferior because it weakens the taste of sweet potato.
Once the potatoes are fork-tender, remove them from the oven and cover them with a clean kitchen towel. Leave the potatoes to steam under this towel for 20 minutes.
Peel, then mash or puree the sweet potatoes until smooth.
Set the mashed (or pureed) sweet potatoes aside**.
In a bowl, mix together the melted butter, sugar, and graham crumbs.
Squeeze a fistful of the crumbs together to check that the mixture is the proper consistency: If the crust holds together in a firm clump, it's ready. On the contrary, if your crumbs stay crumby- add a couple more teaspoons of melted butter; if it oozes butter add more graham crumbs to soak up the excess fat.
Use the bottom of a measuring cup to press the graham cracker mixture into a 9" springform pan.
Bake the crust for 10 minutes in a 350°F oven.
Remove the baked crust from the oven to cool. Once it's cool, wrap the pan in two layers of heavy duty aluminum foil, then set aside.
Bring a pot of water (approx 4 cups) to boil while you prepare the cheesecake batter.
Combine the ground cinnamon, nutmeg, and cloves, the salt, and cornstarch in a small bowl. Set this aside.
In a large mixing bowl, blend together the cream cheese, sugar, lemon zest, and vanilla bean paste on low speed, until smooth.
Add the eggs- one at a time- to the bowl, making sure to scrape down the bowl after each egg is incorporated.
After you've added all of the eggs, slowly mix in the mashed sweet potatoes and the heavy cream until blended.
Finally, add the spice blend you mixed earlier. Blend just until the spices are incorporated. Be sure not to mix the batter too long after adding the cornstarch.
After the sweet potato cheesecake batter has been mixed, place the foil-wrapped cheesecake pan into a larger pan that has at least two inches of clearance on the sides of the cheesecake pan.
Pour the cheesecake batter into the prepared cheesecake pan.
Carefully pour the boiling water into the larger (exterior) pan which the cheesecake pan is sitting in. Be careful to avoid splashing water into the cheesecake batter.
Place the pans into your preheated oven and bake the cheesecake for 1 hour.
Once the baking time has elapsed, turn the oven off and prop open the oven door with a wooden spoon. Allow the cheesecake to cool slowly in the oven for another hour.
After the final hour, remove the cheesecake from the oven and the water bath. Remove the protective foil and allow the sweet potato cheesecake to cool to the touch on the countertop.
Transfer the pan to the fridge and allow it to chill for 8-24 hours.
Toast the pecan halves for 10 minutes in a 350°F oven. Allow them to cool after they've toasted.
Remove the springform collar from the cheesecake, then decorate the top of the chilled cheesecake with a single layer of the toasted pecans.
Return the sweet potato cheesecake to the fridge while you prepare the praline toffee.
In a large pot with sloping sides***, stir together the white and brown sugars, baking soda, the evaporated milk, and the vanilla bean paste until the sugar is dissolved- this should take about 5 minutes.
While you're stirring, heat the mixture over medium heat to bring it to a boil.
Brush the sides of the pot with a pastry brush- dipped in water- to remove any sugar crystals from the sides. (If left on the sides of the pot, the sugar crystals will drop back into the liquid, which will cause it to seize up- or crystallize).
Clean the brush in the water each time you brush down a part of the pot. There should be no remaining sugar crystals when you're done.
After the sides are clean, leave the sugar to come to a boil- without stirring- until the mixture reaches 230°F, or until the mixture, when drizzle back into the pot from the lifted spoon, looks stringy or drips reallllllly slowly- almost clinging to the spoon.
Once it reaches the proper temperature, remove it from the stove.
Add the unsalted butter to the toffee and stir rapidly- the mixture will bubble up, so be careful.
As you stir, the mixture will go from foamy- to dark- to opaque. Once it appears opaque, stop stirring.
Drizzle the praline topping over the pecan-topped cheesecake. Save the rest for drizzling on individual slices after serving.
Store the sweet potato cheesecake in the refrigerator until ready to serve. Enjoy it within 72 hours after baking.
A tip on storing: after cutting slices from a whole cheesecake, press a piece of plastic film or wax paper against the exposed cheesecake to keep it from developing a crust.
*If you're using canned sweet potatoes: Rinse and drain the sweet potatoes thoroughly prior to mashing them to rid the potatoes of their sugary syrup.
**The raw sweet potatoes may be baked, peeled, and mashed up to 6 months in advance. Keep mashed sweet potatoes stored in freezer-safe bags and frozen until ready to use.
***Using a large pot is very important because, later on in the recipe, the mixture is going to bubble and expand. If you've ever been burnt with molten-hot sugar, you will understand why we need to be careful.
****The praline toffee may be made up to a week in advance. Don't add the pecans to the topping. Keep the topping stored in an air-tight container in the refrigerator. Warm it in a hot water bath, or in the microwave until it's pourable.