Pulse black walnuts in a food processor 8 to 10 times or until finely ground; set aside.
Beat butter at medium speed with an electric mixer until creamy; gradually add granulated sugar, beating until light and fluffy. Add egg yolks and vanilla, beating just until blended.
Sift together flour, baking powder, and salt; add to butter mixture alternately with milk, beginning and ending with flour mixture. Beat batter at low speed just until blended after each addition.
Beat egg whites at medium speed with an electric mixer until stiff peaks form; fold into batter. Fold ground walnuts into batter. Spoon batter evenly into a greased and floured 10-inch Bundt pan.
Bake at 350° for 50 minutes or until a wooden pick inserted in center comes out clean. Cool in pan on a wire rack 10 minutes; remove from pan, and cool completely on wire rack. Sprinkle evenly with powdered sugar. Serve with vanilla ice cream and sliced fresh strawberries, if desired.