Drain the potato water in a colander and rinse them under cold, running water. Once drained, arrange the potatoes in a single layer on a sheet pan lined with paper towels and pat dry with more paper towels. Make sure to dry the potatoes as much as possible. Preheat the frying oil to 300°F. Line a second sheet pan with paper towels for draining the fries. Have a large stainless steel bowl nearby for tossing the fries in seasoning as they finish draining.
Par-cook the french fries in batches- to avoid crowding the pan- for 3-5, or until they are tender. They should have no color on them (save for the skin) when you remove them from the oil.
When the fries are finished par-cooking, carefully transfer the fries from the pan to the sheet pan to drain. Allow the fries to cool completely while you par-cook the remaining potatoes.
Once all of the fries have been par-cooked, increase the oil's temperature to 375°F.
Fry the french fries in small batches and use your spider to shift the fries around so they don't stick together. Fry for 4-5, or until the fries are golden brown and rise to the top of the oil.
Remove the finished fries from the oil and place them on a paper towel lined pan to drain away any excess oil.Toss the drained french fries in a bowl with a pinch of salt, a pinch of chopped rosemary, and a few twists of freshly ground black pepper to coat them evenly.
Transfer the seasoned fries to a cooling rack set atop a sheet pan and keep them warm in a low-temperature oven- this will ensure your fries stay as crispy as possible while you fry the remaining batches of french fries.
Serve your french fries while hot, with a sidecar of the Lemon Aioli. Pour some of your aioli dip into a prep bowl for dipping the fries in.