Preheat oven to 350°F (180°C). Spray 3 (9-inch) round cake pans with baking spray with flour.

In the bowl of a stand mixer fitted with the paddle attachment, beat butter and brown sugar at medium speed until fluffy, 3 to 4 minutes, stopping to scrape sides of bowl. Add eggs, one at a time, beating well after each addition. Beat in vanilla.

In a medium bowl, whisk together flour, baking powder, and salt. With mixer on low speed, gradually add flour mixture to butter mixture alternately with milk, beginning and ending with flour mixture, beating just until combined after each addition. Divide batter among prepared pans, smoothing tops with an offset spatula.

Bake until a wooden pick inserted in center comes out clean, 25 to 30 minutes. Let cool in pans for 10 minutes. Remove from pans, and let cool completely on wire racks.

Place 1 cooled cake layer on a cake plate. Brush layer with about 2½ tablespoons (45 grams) Simple Syrup. Place ½ cup (95 grams) Brown Sugar Buttercream in a small pastry bag; cut a ½-inch opening in tip. Pipe a border around edge of cake layer. Spoon half of Pecan Pie Filling (about 1¼ cups [about 337 grams]) on cake layer, and gently smooth until even and reaches piped border. Top with second cake layer, and repeat procedure. Top with remaining cake layer, and brush with remaining Simple Syrup. Reserve 1½ cups (285 grams) Brown Sugar Buttercream to decorate top of cake. Spread remaining buttercream on top and sides of cake. Using a cake comb, comb sides of cake. Gently press pecans high on sides of cake and a few at bottom, if desired. Place reserved buttercream in a large pastry bag fitted with a ½-inch open star tip (Ateco #824), and pipe a border around edge of cake. Cover and refrigerate until ready to serve. Allow to come to room temperature before serving.