Pour apple pie filling into a bowl. Cut each apple slice into thirds using a spoon.
Place cookie butter in a microwave-safe bowl. Microwave in 5-second intervals, stirring after each interval, until pourable but still thick, 10 to 15 seconds.
Place ice cream in the bowl of a stand mixer fitted with the paddle attachment. Blend on low speed until uniformly softened, 10 to 15 seconds. Add apples; blend until incorporated. Fold in cookie butter gently to create ribbons.
Line a rimmed 9x13-inch baking sheet with aluminum foil. Spread ice cream mixture on top.
Freeze ice cream and cookies until firm, 5 hours to overnight.
Remove cookies from the freezer. Line a baking sheet with parchment paper. Place 6 cookies on top.
Remove ice cream from the freezer. Cut ice cream into rounds using a 3-inch cookie cutter. Transfer ice cream rounds to the cookies using a spatula or by pressing them out of the cookie cutter with a spoon. Press another cookie on top.
Place baking sheet in the freezer; chill until ice cream cookie sandwiches are firm, 1 to 2 hours.
Place 1 sandwich into each sandwich bag; fold the edge and crease to seal. Freeze until serving. Peel down bag as you eat, keeping the bag underneath to catch drips.