For the Shortbread-Style Crust:

1. Preheat oven to 350°F (176°C). Grease a 9-inch springform pan.
2. In a food processor, combine gluten-free flour, sugar, salt, and lemon zest. Pulse a few times to mix.
3. Add cold butter and vanilla extract, then pulse until the mixture forms coarse crumbs (it should not become dough).
4. Pour into the prepared pan and press firmly into an even layer. Use a spoon or measuring cup for an even surface.
5. Poke holes with a fork to prevent air bubbles.
6. Bake for 17-20 minutes, or until lightly golden. Let cool for 15 minutes before adding cheesecake filling.

For the Oatmeal Cookie-Style Crust:

1. Preheat oven to 350°F (176°C). Grease a 9-inch springform pan.
2. In a food processor, pulse oats, coconut sugar, cinnamon, and salt until combined.
3. Add softened butter and vanilla extract, then process for 30 seconds until the mixture holds together when pinched.
4. Transfer to the pan and press evenly over the bottom.
5. Bake for 14-16 minutes, until lightly browned. Let cool for 5-10 minutes before adding cheesecake filling.