Preheat oven to 350°F (175°C) and grease a 9-inch springform pan; line the bottom with parchment paper. In a bowl, cream butter and sugar until light and fluffy, then beat in the egg and vanilla.

In a separate bowl, whisk together flour, baking powder, and salt. Gradually add dry ingredients to wet, mixing until just combined to form a soft dough. Press the dough evenly into the bottom of the prepared springform pan.

Bake the crust for 10-12 minutes, or until lightly golden, then remove from oven and let cool slightly while preparing the filling.

Reduce oven temperature to 325°F (160°C). In a large bowl, beat softened cream cheese and sugar until smooth and creamy, then mix in sour cream, vanilla extract, and lemon juice if using.

Add eggs one at a time, mixing on low speed until just combined after each addition; avoid overmixing. Pour the cheesecake batter over the cooled sugar cookie crust in the springform pan.

Bake for 60-70 minutes, or until the edges are set and the center jiggles slightly. Turn off the oven, crack the door open, and let the cheesecake cool inside for 1 hour.

Remove the cheesecake from the oven, run a knife around the edge of the pan to prevent cracking, and let it cool completely on a wire rack. Once cooled, cover and refrigerate for at least 6 hours, or preferably overnight, before serving.