How to Make It
Prepare the Candied Pecans: Preheat oven to 300°F. Whisk together 2 tablespoons light brown sugar, 1 tablespoon granulated sugar, 1/4 teaspoon salt, and 1 egg white in a medium bowl until foamy. Add pecan halves; toss well to coat. Spread pecan halves in a single layer on a baking sheet lined with parchment paper. Bake in preheated oven until browned, 25 to 28 minutes, stirring after 15 minutes. Cool completely, about 30 minutes. (Pecans will become crisp when cool.)
Prepare the Cake: Increase oven temperature to 350°F. Whisk together 3 cups flour, 1 tablespoon baking powder, and 3/4 teaspoon salt in a bowl. Beat 2 cups granulated sugar and 1 cup butter in a large bowl of a stand mixer at medium speed until light and fluffy, about 4 minutes. Add eggs and egg yolks, 1 at a time, beating well after each addition. Add flour mixture to butter mixture alternately with milk, in 5 additions, beginning and ending with flour mixture. Beat at low speed after each addition. Beat in pecan liqueur and 1 teaspoon vanilla. Divide batter evenly between 2 (9-inch) greased and floured round cake pans.
Bake in preheated oven until a wooden pick inserted in the center comes out clean, 28 to 30 minutes. Cool in pans on a wire rack 10 minutes. Remove cakes from pans; cool completely on wire rack, about 30 minutes.
Prepare the Filling: Combine 3/4 cup dark brown sugar, 6 tablespoons butter, and 1/4 cup heavy cream in a small saucepan over medium-low, and cook, stirring occasionally, until butter melts; bring to a boil. Cook, stirring constantly, 1 minute. Remove pan from heat; add powdered sugar and 1/4 teaspoon vanilla. Beat at low speed until mixture thickens to spreading consistency, about 1 minute. Stir in chopped toasted pecans.
Prepare the Buttercream: Whisk together 1 cup light brown sugar, 1 cup milk, 1/2 cup flour, and 1/4 teaspoon salt in a small saucepan until smooth. Place pan over medium-high, and cook, whisking constantly, until mixture is very thick and bubbly, 4 to 5 minutes. Spoon mixture into a bowl; place bowl in freezer, uncovered, until mixture is cold, about 20 minutes, stirring every 5 minutes.
Beat 1 cup butter with an electric mixer at medium speed, using whisk attachment, until creamy and smooth, about 2 minutes. Add cold brown sugar mixture, 1 tablespoon at a time, beating well after each addition. Add 1 1/2 teaspoons vanilla, and beat at high speed until light and fluffy, about 5 minutes.
Place 1 cake layer on a serving plate; spread Filling evenly over top, leaving a 1/2-inch border. Place remaining cake layer on top, pressing lightly. Spread Buttercream on top and sides of cake. Arrange Candied Pecans over top.