Pour melted butter into an 8-inch square baking pan coated with cooking spray; sprinkle with brown sugar. Bake at 350° for 2 minutes. Remove from oven, and top with pecans and cranberries.
Lightly spoon flour into dry measuring cups; level with knife. Combine flour, baking powder, and salt in a bowl; stir with whisk.
Place sugar and butter in a large bowl; beat with a mixer at medium speed until well blended. Add egg yolks, 1 at a time, beating well after each addition. Stir in vanilla.
Add flour mixture and milk alternately to butter mixture, beginning and ending with flour mixture; mix after each addition. Beat the egg whites with a mixer at high speed until stiff peaks form using clean, dry beaters; fold into batter.
Spread batter over cranberries. Bake at 350° for 45 minutes. Cool in pan for 5 minutes on a wire rack. Loosen edges of cake with a sharp knife. Place a plate upside down on top of cake pan; invert onto plate.
Combine whipped topping and cognac, and serve with warm cake.