Lightly spoon the flour into dry measuring cups; level with a knife. Combine 2 cups flour, sugar, salt, nutmeg, and yeast in a large bowl. Add the milk and butter, stirring with a wooden spoon until smooth. Add the eggs, 1 at a time, beating well after each addition. Stir in vanilla. Add 1 cup flour, stirring until smooth.
Scrape batter into a 13 x 9-inch baking pan coated with cooking spray. Coat dough with cooking spray. Cover and let rise in a warm place (85°), free from drafts, 1 hour or until dough is doubled in size (batter should become bubbly on the surface).
Preheat oven to 350°.
Bake at 350° for 30 minutes or until golden brown and a toothpick inserted in center comes out clean. Cool in pan on a wire rack. Sprinkle with powdered sugar. Cut in squares.