Place egg whites in a large bowl; let stand at room temperature for 30 minutes. Sift flour twice; set aside. Add cream of tartar and vanilla to egg whites; beat on medium speed until soft peaks form. Gradually beat in sugar, about 2 tablespoons at a time, on high until stiff glossy peaks form. Gradually fold in flour, about 1/4 cup at a time. Fold in pecans.
Gently spoon into an ungreased 10-in. tube pan. Cut through batter with a knife to remove air pockets. Bake on the lowest oven rack at 350° for 35-40 minutes or until lightly browned and entire top appears dry.
Immediately invert pan; cool completely, about 1 hour. Run a knife around side and center tube of pan; remove cake. Serve with whipped cream if desired.