In a large bowl, beat butter and ¾ cup sugar with a mixer at medium speed until fluffy, 3 to 4 minutes, stopping to scrape sides of bowl. Gradually add egg, beating until well combined and stopping to scrape sides of bowl. Beat in extract.
In a medium bowl, whisk together flour, baking powder, and salt. Add flour mixture to butter mixture, and beat at low speed just until combined, 1 to 2 minutes, stopping to scrape sides of bowl.
In a small bowl, stir together cream cheese and remaining 2 tablespoons sugar. Cover dough and cream cheese mixture with plastic wrap, and freeze for 25 minutes.
Preheat oven to 350°. Line rimmed baking sheets with parchment paper.
Scoop dough by level tablespoonfuls, and shape into 2-inch disks. Spoon 1½ teaspoons cream cheese mixture in center of half of disks; cover with remaining disks, and crimp edges closed. Gently shape into balls; roll balls in ½ cup crushed candies. Place 2½ inches apart on prepared pans. Gently flatten balls to ¾-inch thickness, pressing together any cracks in edges, if necessary.
Bake until edges are set and bottoms are golden brown, 12 to 14 minutes. Gently press remaining ½ cup crushed candies into top of cookies. Let cool on pans for 3 minutes. Remove from pans, and let cool completely on wire racks. Store in an airtight container for up to 3 days.
Notes
*We used Bob's Olde Timey Peppermint Candy Pure Sugar Sticks.
Kitchen Tip: If crushed peppermint isn’t sticking to dough as much as you’d like, lightly spray dough with warm water before rolling in candy. Do not substitute hard peppermint candy.
Recipe by Paula Deen Magazine at https://pauladeenmagazine.com/cream-cheese-stuffed-peppermint-sugar-cookies/