Preheat oven to 325°F (170°C). Lightly spray 2 (6-inch) round cake pans with baking spray with fl our. Line bottom of pans with parchment paper.
In the bowl of a stand mixer, whisk together flour, sugars, baking powder, salt, cinnamon, and nutmeg by hand. Add butter and 1/3 cup (85 grams) cookie butter; using the paddle attachment, beat at low speed until butter and cookie butter are worked into mixture and mixture resembles coarse crumbs.
In a small bowl, whisk together milk, eggs, and vanilla. With mixer on low speed, add about half of milk mixture to flour mixture. Increase mixer speed to medium, and beat until light and fluffy, 2 to 3 minutes. With mixer on medium-low speed, add remaining milk mixture, beating until combined and stopping to scrape sides of bowl. Divide batter between prepared pans (about 1½ cups or 390 grams each). Using a small offset spatula, spread batter into an even layer.
Bake until a wooden pick inserted in center comes out clean and an instant-read thermometer inserted in center registers 200°F (93°C) to 205°F (96°C), 40 to 45 minutes. Let cool in pans for 10 minutes. Remove from pans, and let cool completely on a wire rack.
Level cooled cake layers, if desired. Place 1 cake layer on a cake board or serving platter. Spread ¾ cup (140 grams) Cookie Butter Buttercream onto cake layer, and top with remaining cake layer. Spread remaining buttercream on top and sides of cake.
In a small microwave-safe bowl, heat remaining 1 tablespoon (15 grams) cookie butter on high until soft and thinned out slightly. Dot cookie butter onto sides of cake; using an offset spatula, spread cookie butter into buttercream. Garnish with cookie crumbs and pieces, if desired. Refrigerate for at least 30 minutes before serving. If refrigerating for longer than 1 hour, let cake stand at room temperature for 20 to 30 minutes before serving. Refrigerate in an airtight container for up to 3 days.