Preheat the oven to 350°F. Line a baking sheet with parchment paper.
Cream the butter, cream cheese, powdered sugar, and granulated sugar together until light and fluffy, about 3 minutes. Add the vanilla and almond extract and mix until combined.
In a separate bowl, whisk together the flour, cornstarch, and salt. Add the dry ingredients to the butter mixture and mix just until a soft dough forms.
Roll about 1 tablespoon of dough into a ball, then slightly flatten it. Using the back of a ½ teaspoon measuring spoon, press gently into the center to create an indent, smoothing the edges if needed.
Place on the center rack of the oven, not too high or low. Bake for 9-11 minutes, Do not over bake, the cookies should remain pale with little to no color on top. They will continue baking on the baking sheet.
Using the back of a 1 teaspoon measuring spoon, gently reinforce the center indent while the cookies are still warm. Make sure not to press too hard.
Let cool on the baking sheet. Fill with lemon curd, top with powdered sugar or glaze/icing if desired.
See storage in notes.