Preheat your oven to 350°F. Bring a pot of water to a boil for the bain-marie (water bath) which you'll bake the flan in. Have a pan (larger than the pan you'll prepare the flan in) ready to create the bain-marie.
Prepare the Caramelized Sugar
In a non-stick pan, add the water to the pan, then, right into the center of the pan, pour the sugar. This keeps the sugar from the sides of the pan. Gently stir the sugar and water together using a wooden spoon and bring the mixture up to a gentle simmer over medium heat.
Once the sugar begins to simmer, stop stirring. If, at this point, you see any sugar crystals on the sides of the pan, use a wet pastry brush to brush the crystals down into the pot. Boil the sugar 7 1/2-8 minutes, or until the sugar takes on a deep amber color (a candy thermometer should read 320°F- 350°F).
Once the sugar reaches the amber color, carefully pour it into a 8" or 9" cake pan. The pan will become extremely hot when the sugar is poured in, so use a towel or oven mitt to hold onto the pan to keep from burning yourself. Swirl the sugar onto the bottom of the pan.
Set the pan aside to allow the sugar to cool and harden while you prepare the custard.
Prepare, then Bake Vanilla Flan
Pour the eggs into your blender. Pulse the eggs for 30 seconds to beat them slightly.
Next, pour the sweetened condensed milk, evaporated milk, water, vanilla bean paste (or vanilla extract) into the blender. Blend the mixture for 1 minute, or until smooth.
Once smooth, pour the mixture through a sieve into the sugar-rimmed pan to remove any mucous-like strings of egg and to reduce the amount of bubbles and foam created by the blender.
Place the flan pan into the larger pan, then fill the outer pan with boiling water until it reaches half-way up the sides of the flan pan. Take care not to splash any water into the custard.
Carefully slide the pans into the pre-heated oven and bake for 1 hour. The flan will still jiggle like jello when fully baked. After 45 minutes of baking check the color of the flan: if it looks like it's browning too much, lay a piece of foil over the pans to slow down the caramelization.
Chill the Baked Flan
After the baking time has elapsed, carefully remove the larger pan from the oven, then remove the flan pan from the water-filled one. Allow the flan to cool completely on the countertop before covering the pan with plastic wrap and refrigerating.
Refrigerate the flan for 24-48 hours. The longer, the better as it allows time for all of the sugar to liquify.
Flip to Serve
Before turning out the flan, loosen the sides of the custard from the pan. To do this, take a knife, dipped in hot water, and run it along the sides: between the flan and the pan. Invert a plate onto the pan and flip the two over. The flan should schloop right out of the pan. The caramelized sugar liquid will start to ooze from the pan onto the plate.
If you don't hear the schloop or see the caramel, the flan isn't out of the pan. Flip it back over and dip the bottom of the pan into 2" of hot water to loosen the sides, then attempt the flip again. If it doesn't schloop flip it back over and enjoy it with a spoon, instead.
Leave the pan inverted for about 5 minutes to coat the flan in as much of the caramel as possible.Slice the flan into serving sizes and serve cold: straight from the fridge. You can also top your slices with a dollop of whipped cream or a handful of fresh berries.
Store leftover flan lightly covered in plastic wrap in the fridge for 3 to 4 days.
To make individual flanes:
Divide the caramelized sugar equally among the cups of a muffin tin.
Strain the custard into a larger bowl first.
Pour the custard into the muffin tin in equal measures.
Set the muffin tin on a flat sheet pan or baking dish filled with an inch of hot water.
Bake for 30-40 minutes at 350°F.
Chill for 8-48 hours and turn out onto a large platter.
Divide the caramelized sugar equally amongst 4 ramekins.
Strain the custard into the prepared ramekins.
Set the ramekins into a baking dish filled with 1 1/2" of hot water.
Bake for 45 minutes to 1 hour.
Chill for 8-48 hours and turn out onto individual plates.
Notes on Caramelizing the Sugar:
If the sugar doesn't firm up after a minute or two of cooling, you didn't boil it long enough. Unless you absolutely have to have a perfect flan, bake it as is: it's still totally fine to proceed.
If you've overcooked your sugar and it smells bitter and acrid, throw it away and start again. Place the pot in your sink and pour hot water into it from the faucet. Keep your hands, arms, and face from the pot because the steam will be intense and the water and sugar will bubble up. Allow the water to melt the sugar. If it's taking too long, place the pan, filled with water over the stove and bring it to a boil to dissolve the caramel faster.
Notes on Baking the Flan:
After it's baked, the flan is not going to be solid. So, if yours still jiggles- think jello- that's perfectly fine. As the flan cools in the fridge, it will grow more solid.
If, however, the custard is sloshing around after an hour of baking, the issue may be that some water was introduced to the custard while you were adding it to the larger pan. As a result of that added water, the flan will not set. Allow the custard to cool before chilling it completely in the fridge. When ice-cold, churn it in an ice cream machine to make flan ice cream.