Line a small cookie sheet with parchment paper; set aside. Shape edible cookie dough into 6 balls using a slightly rounded tablespoon of dough for each. Place on prepared cookie sheet. Flatten each to a 2-in. round. Freeze until ready to assemble cookies.

For cookies, whisk together flour, oats, baking powder and salt in a medium bowl; set aside.

Beat butter in a large mixing bowl with an electric mixer on medium for 30 seconds. Add granulated and brown sugars, peanut butter and vanilla. Beat until combined, scraping side of bowl occasionally. Beat in egg until combined. Stir in flour mixture until combined. Add blue and red food coloring gels. Knead until dough is evenly colored. Stir in baking chips.

Line a large cookie sheet with parchment paper. Shape dough into 12 balls. Flatten each ball into a 3-in.-round disk on the prepared cookie Cover and refrigerate for 30 minutes.

Place oven rack in center of oven. Preheat oven to 350°. Coarsely chop 3 chocolate sandwich and chocolate chip cookies; place in small bowl and set aside.

To assemble cookies, top each of 6 cookie dough disks with 1 frozen edible cookie dough round and 1 remaining chocolate sandwich cookie. Then top with remaining 6 cookie dough disks. Press edges together to seal in edible cookie dough; smooth any cracks in the dough. Sprinkle crumbled cookie mixture onto tops; gently press into dough. Place filled cookies 2 in. apart on the prepared large cookie sheet.

Bake for 16 to 18 minutes or until tops are firm to the touch. Cool cookies on cookie sheet for 3 to 4 minutes. Transfer cookies to wire rack and cool completely. Store in an airtight container in the refrigerator up to 5 days. To soften centers of chilled cookies, microwave each cookie on HIGH for 15 to 20 seconds just before serving.