Step 1: In a large bowl or stand mixer, cream together the softened butter and granulated sugar for 3-5 minutes until the mixture is pale and very fluffy.
Step 2: Add the eggs one at a time, beating well after each addition, then stir in the sour cream and vanilla extract until combined.
Step 3: In a separate bowl, whisk together the flour, cornstarch, baking powder, and salt.
Step 4: Gradually add the dry ingredients to the wet ingredients, mixing on low speed just until no more flour streaks remain; do not overmix.
Step 5: Wrap the dough in plastic wrap and refrigerate for at least 2 hours, or preferably overnight.
Step 6: Preheat your oven to 350°F (175°C) and line baking sheets with parchment paper. Roll out the dough to 1/4 inch thickness on a floured surface.
Step 7: Cut out shapes and bake for 8-10 minutes. Remove from the oven while they are still pale and let cool on the sheet for 5 minutes before transferring to a wire rack.