Sift together flour, dry milk, baking powder, and salt. Set aside.
Using an electric mixer, cream the butter and stir in vanilla. Gradually add sugar; beat until light and fluffy. Add well-beaten eggs, blending until smooth. Add dry ingredients and mix until well blended. Divide dough in half. Stir cocoa into one half, blending well. Shape each half into a rectangle, about 2" x 2" x 6". Tightly wrap in waxed paper. Chill at least 30 minutes.
Unwrap dough; cut each rectangle into quarters, lengthwise. Alternately place dark and white quarters side by side to form checker design. Rewrap in waxed paper and chill slightly.
Slice dough into 1/8-inch pieces and place on ungreased cookie sheet. Bake at 350° for 12 minutes.