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.
Worthy of a special occasion... if that special occasion is an after-school snack! Occasionally I make this for my kids and have it ready when they get home from school. I like it because it is a treat... but not too bad for you. It has only healthy fats (no sat or trans fats-- I use canola oil it it). True, it has no fiber or anything else good to speak of... but serve it with some berries on the side and a glass of milk and it's not too bad. Also, I skip the frosting and just serve it warm just out-of-the-oven like a brownie. You could sprinkle some powdered sugar on top for a finished look if you'd like.
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