Sift together flour, 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, almond butter and vanilla. Beat until combined, scraping side of bowl occasionally. Beat in egg until combined. Stir in flour mixture until combined; stir in ¼ cup chopped toffee.

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 sheet. Cover and refrigerate for 45 minutes.

Meanwhile, for ganache, place chopped dark chocolate in a medium bowl; set aside. Microwave cream in a 1-cup microwave-safe measuring cup on HIGH for 30 to 60 seconds or until very hot but not boiling. Pour cream over chocolate; let stand for 20 seconds. Whisk until melted and smooth. Cool chocolate mixture for 20 minutes or until slightly thickened, stirring occasionally.

Line another cookie sheet with parchment paper; set aside. Spoon chocolate ganache into a disposable pastry bag; cut off a ½-in. tip from the bag. Pipe 6 (2½-in.) rounds onto prepared cookie sheet. Freeze for 20 to 30 minutes or until completely set.

Place oven rack in center of oven. Preheat oven to 350°. To assemble cookies, top 6 cookie dough disks with chocolate ganache rounds. Then top with remaining 6 cookie dough disks. Press edges together to seal in ganache; smooth any cracks in the dough. Place filled cookies 2 in. apart on the prepared large cookie sheet.

Bake for 14 to 16 minutes or until golden brown around bottom edges. Remove from oven; top with remaining ¼ cup chopped toffee. Cool cookies on cookie sheet for 5 minutes. Transfer cookies to a 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.