Bake pecans in a shallow pan at 350°, stirring occasionally, 8 minutes or until toasted. Cool completely. Process 1/4 cup pecans in a food processor until finely chopped. Set aside.
Beat butter and shortening at medium speed with an electric mixer until fluffy; gradually add 3/4 cup granulated sugar, beating well. Add egg yolks, 1 at a time, beating until blended after each addition. Stir in vanilla bean paste.
Combine flour and baking soda; add to butter mixture alternately with buttermilk, beginning and ending with flour. Beat at low speed until blended after each addition.
Beat egg whites at medium speed until soft peaks form; add remaining 1/4 cup granulated sugar, 1 tablespoon at a time, beating until stiff peaks form. Fold one-third of egg whites into batter; fold in remaining egg whites and 1/2 cup toasted pecans. Spoon batter into paper-lined muffin cups, filling two-thirds full.
Bake at 350° for 22 minutes or until a wooden pick inserted in center comes out clean. Cool in pans 5 minutes on a wire rack. Remove from pans, and cool completely.
Combine reserved 1/4 cup finely chopped pecans and brown sugar in a small bowl. Spread a generous 2 tablespoons Browned Butter Frosting onto each cupcake. Sprinkle tops of cupcakes with pecan-sugar mixture.