In the bowl of a stand mixer fitted with the paddle attachment, beat butter and sugar at medium speed until fluffy, 3 to 4 minutes, stopping to scrape sides of bowl. Add eggs, one at a time, beating well after each addition. Beat in peppermint extract.
In a medium bowl, whisk together flour, cocoa, baking powder, and salt. With mixer on low speed, gradually add flour mixture to butter mixture, beating just until combined and stopping to scrape sides of bowl. Cover and refrigerate until dough doesn’t stick to your fingers when pinched, 30 to 45 minutes.
Preheat oven to 350°F (180°C). Line 4 rimmed baking sheets with parchment paper.
Using a 1½-tablespoon spring-loaded scoop, scoop dough (about 26 grams each), and roll into balls. Press balls into 2½-inch disks. Place 2 teaspoons (12 grams) Peppermint Pastry Cream in center of half of disks; cover with remaining disks, and crimp edges closed. Gently shape into balls, and place on prepared pans; gently press into 2¼-inch disks, pressing together any cracks in edges, if necessary. Brush tops of cookies with 2 tablespoons (30 grams) water; top with candies.
Bake until edges are set and tops look dry, 12 to 14 minutes. (See Note.) Carefully top with any remaining candies. Let cool completely on pans.
Notes
If you need to bake the cookies in batches, refrigerate any disks that are waiting to be baked.
Recipe by Bake from Scratch at https://bakefromscratch.com/peppermint-custard-stuffed-chocolate-cookies/