Prep the pan and oven. Heat the oven to 325°F (163°C).
Wrap the outside of a 9-inch springform pan with two layers of heavy-duty foil, covering the bottom and sides tightly to prevent water from seeping in. Lightly grease the inside of the pan.
Make the crust. In a bowl, mix the gluten-free crumbs, sugar, and salt. Stir in melted butter until the mixture looks like damp sand and holds when pressed.
Press firmly into the bottom and 1 inch up the sides of the pan. Use a flat-bottomed glass to compact.
Pre-bake the crust. Bake for 10 minutes. Remove and cool on a rack while you make the filling.
Keep the oven at 325°F.
Soften the cream cheese properly. Make sure the cream cheese is fully at room temperature. This prevents lumps and overmixing later.
Mix the base gently. In a stand mixer with the paddle (or a hand mixer on low), beat the cream cheese, sugar, salt, and cornstarch on low until smooth and creamy, about 2 minutes. Scrape the bowl and paddle as needed.
Avoid whipping air into the batter.
Add eggs with care. Add the eggs and yolk one at a time on low speed, mixing just until combined after each addition. Scrape the bowl once more.
Finish the batter. Add sour cream, lemon juice, and vanilla. Mix on low just until smooth.
If you see a few stubborn lumps, press them out with a spatula rather than overmixing.
Set up the water bath. Place the foil-wrapped pan in a large roasting pan. Pour the batter into the crust and smooth the top. Set the roasting pan on the oven rack, then pour hot water into the roasting pan until it comes halfway up the sides of the springform.
Bake low and slow. Bake for 60–75 minutes.
The edges should look set, and the center should wobble slightly when you gently nudge the pan. If the top is browning, tent loosely with foil in the last 15 minutes.
Use a knife trick to prevent cracks. Remove the roasting pan from the oven and carefully lift out the cheesecake. Immediately run a thin knife around the inside edge of the pan to release the cake from the sides.
This prevents tension and cracks as it cools.
Cool down gradually. Let the cheesecake cool in the pan on a rack for 1 hour. Then transfer to the fridge, uncovered, for at least 6 hours, preferably overnight. Avoid moving it around during this time.
Unmold and serve. Remove the springform ring.
For clean slices, warm a sharp knife under hot water, wipe dry, and slice, cleaning the blade between cuts. Add berries or whipped cream if you like.