Prep. Preheat oven to 350°F. Butter and flour a 13x9-inch baking pan.
Mix dry ingredients. Sift together flour, baking soda, baking powder, cinnamon, nutmeg, cloves, ginger, and salt. Set aside.
Cream butter and sugar. Beat butter until fluffy, about 1 minute. Gradually add sugar and beat on high until light and fluffy, about 3 minutes.
Add egg yolks. Add egg yolks one at a time, beating well after each. Mix in vanilla.
Combine wet and dry. Alternately add dry ingredients and milk in three additions, starting and ending with dry ingredients. Mix just until combined.
Fold in egg whites. Whip egg whites until stiff but not dry. Gently fold into batter.
Bake. Pour batter into prepared pan and smooth top. Bake 25-30 minutes, until center springs back when pressed and toothpick comes out clean. Cool completely in pan.