Combine first 5 ingredients in a medium bowl; beat at medium speed of a mixer until well-blended. Combine flour, 1/3 cup cocoa, salt, and baking powder; stir well. Add flour mixture to sugar mixture, beating just until blended.
Pour batter into a 9-inch round cake pan coated with cooking spray. Bake at 375° for 25 minutes or until wooden pick inserted in center comes out clean. Cool in pan 10 minutes; remove from pan, and let cool completely on a wire rack.
Combine powdered sugar and milk; beat at low speed until smooth. Spread 1/2 cup powdered sugar glaze over top of cake. Add 1 teaspoon cocoa to remaining sugar mixture, stirring with a whisk until blended. Spoon into a small zip-top plastic bag. Snip off 1 corner of bag, making a small hole. Starting in center of cake, pipe frosting in 4 concentric circles. Starting at center circle, pull a wooden pick or tip of a knife through circles at regular intervals to edge of cake to form a "web" design.