Adjust oven rack to middle position and heat oven to 350 degrees. Grease and lightly flour a metal or disposable foil 9-by-13-inch pan. Whisk dry ingredients and spices in a large bowl. Mix milk, eggs and vanilla extract in a 2-cup measuring cup.
Beat softened butter into dry ingredients, first on low, then medium, until mixture forms pebble-sized pieces. Add about 1/3 of the milk mixture and beat on low until smooth. Add remaining milk mixture in two stages; beat on medium speed until batter is just smooth. Add the sugar; beat until just incorporated, about 30 seconds. Pour batter into cake pan.
Bake until a cake tester or toothpick inserted into the cake's center comes out clean, about 40 minutes. Set pan on a wire rack; let cool for 5 minutes. Run a knife around the pan perimeter and turn cake onto rack. Let cool.