1 1⁄2 cups butter, softened
2 1⁄2 cups sugar
3 large eggs
2 large egg yolks
4 cups all-purpose flour
1 tablespoon baking powder
1 teaspoon salt
1 cup whole milk
1⁄2 cup sour cream
1 tablespoon vanilla extract
2 cups firmly packed dark brown sugar
1 cup chilled butter, diced
1 cup heavy whipping cream
1 tablespoon light corn syrup
1 teaspoon salt
5 cups confectioners’ sugar, sifted
2 teaspoons apple cider vinegar
1 teaspoon vanilla extract
Buttered Pecans (recipe follows)
Garnish: 1⁄4 teaspoon kosher salt
Preheat oven to 350°. Spray 3 (9-inch) round cake pans with nonstick baking spray with flour. Line bottoms of pans with parchment paper; spray with nonstick baking spray with flour.
For cake: In the work bowl of a stand mixer fitted with the paddle attachment, beat butter and sugar until fluffy, stopping occasionally to scrape sides of bowl. Add eggs and egg yolks, one at a time, beating well and scraping bowl after each addition. In a medium bowl, whisk together flour, baking powder, and salt. In another bowl, combine milk and sour cream; stir well. With mixer on low speed, add flour mixture to butter mixture in thirds, alternating with milk mixture, beginning and ending with flour mixture. Add vanilla; beat just until blended. (Batter will be thick.) Divide batter among prepared pans (3 level cups per pan).
Bake until a wooden pick inserted in center comes out clean, approximately 30 minutes. Let cool in pans 10 minutes. Remove from pans, and let cool completely on wire racks.
For frosting: In a large heavy saucepan, bring brown sugar, butter, cream, syrup, and salt to a boil over medium heat, stirring constantly. Reduce heat to medium-low; cook 5 minutes, stirring occasionally. Remove from heat.
Gradually add confectioners’ sugar, vinegar, and vanilla, beating at medium speed with an electric mixer until smooth. Let stand until mixture begins to thicken and is slightly cooled, approximately 30 minutes, stirring occasionally. Finely chop 1 cup Buttered Pecans; set aside. Reserve remaining 2 cups pecan halves.
On a cake plate or stand, place one cake layer; top with approximately 3⁄4 cup frosting. Gently spread with an offset spatula, leaving a 1⁄2-inch border, until frosting thickens, 1 to 2 minutes. Sprinkle evenly with half of finely chopped Buttered Pecans. Repeat procedure once. Top with remaining cake layer; spread with approximately 3⁄4 cup frosting. Secure center of cake with a wooden pick. Spread a thin layer of frosting around sides of cake; let stand until set, approximately 20 minutes. Frost top and sides of cake with desired amount of remaining frosting. Remove wooden pick just before serving. Top cake with reserved Buttered Pecans. Sprinkle with 1⁄4 teaspoon kosher salt, if desired.