Step 1: In a large bowl or stand mixer, cream together the softened butter, granulated sugar, and brown sugar until the mixture is light and fluffy (about 3-5 minutes).
Step 2: Add the egg and vanilla extract to the butter mixture and beat until well 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 until just combined. Do not overmix.
Step 5: Wrap the dough in plastic wrap and chill in the refrigerator for at least 1 hour.
Step 6: Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper.
Step 7: Scoop tablespoon-sized portions of dough and roll them into balls. Place them 2 inches apart on the prepared baking sheets.
Step 8: Use your thumb or the back of a small spoon to create an indentation in the center of each dough ball.
Step 9: Fill each indentation with about 1 teaspoon of pistachio cream.
Step 10: Bake for 10-12 minutes, or until the edges are very lightly golden. The centers should still look soft.
Step 11: Remove from the oven and let the cookies cool on the baking sheet for 10 minutes before transferring to a wire rack to cool completely.