In the bowl of a stand mixer fitted with the paddle attachment, beat butter and ¾ cup (150 grams) sugar at medium speed until fluffy, 2 to 3 minutes, stopping to scrape sides of bowl. Beat in egg and peppermint vanilla extract until well combined, stopping to scrape sides of bowl.

In a large bowl, whisk together flour, baking powder, and salt. Add flour mixture to butter mixture all at once; beat at low speed just until combined, stopping to scrape sides of bowl.

In a small bowl, stir together cream cheese and remaining 2 tablespoons (24 grams) sugar until well combined. Cover cream cheese mixture and dough with plastic wrap; freeze for 25 minutes.

Preheat oven to 350°F (180°C). Line 2 rimmed baking sheets with parchment paper.

In a small shallow bowl, place candies.

Using a 1-tablespoon spring-loaded scoop, scoop dough into balls (about 18 grams each); flatten into 2-inch disks. Place 1½ teaspoons (about 9 grams) cream cheese mixture in center of 1 dough disk; cover with a second disk, and crimp edges to seal. Gently shape into a ball; roll in candies. (See Note.) Repeat with remaining dough and remaining cream cheese mixture. Place dough balls 1½ inches apart on prepared pans, and gently flatten to ¾-inch thickness, pressing together any cracks in edges, if necessary.

Bake, one batch a time, until edges are set and bottoms are golden brown, 12 to 15 minutes. Carefully garnish warm cookies with candies, if desired. Let cool on pans for 3 minutes. Remove from pans, and let cool completely on wire racks.