Cream butter in a large mixing bowl; gradually add sugar, beating well. Add eggs, vanilla, and milk; beat well.
Combine 1 cup flour, baking powder, and nutmeg. Add to creamed mixture, mixing well. Gradually add remaining flour. Divide dough in half; wrap in waxed paper, and chill at least 30 minutes.
Roll half of dough to 1/4-inch thickness on a floured surface. Cut dough with a 2 1/2-inch biscuit cutter. Place on a lightly greased baking sheet. Bake at 350° for 12 minutes or until edges are lightly browned. Cool cookies on a wire rack. Repeat rolling, cutting, and baking procedure with remaining dough.