Combine first 3 ingredients in a large bowl; stir well. Spread batter into a 15 x 10-inch jelly-roll pan coated with cooking spray. Bake at 350° for 20 minutes; let cool completely in pan on a wire rack. Cut brownie into 7 (10 x 2-inch) strips; trim dry edges, if needed.
Coat a deep, round bottom 2 1/2-quart bowl with cooking spray; line with heavy-duty plastic wrap, allowing wrap to extend over edge of bowl. Arrange brownie strips in bottom and up sides of bowl, trimming strips as needed and pressing edges of strips together (inside surface of bowl should be completely covered). Reserve remaining brownie strips.
Spoon 1 cup coffee yogurt into the bottom of brownie-lined bowl. Fold caramel syrup into vanilla yogurt, and spoon over coffee yogurt layer, spreading evenly. Top with remaining coffee yogurt, spreading evenly. Cover top layer completely with the reserved brownie strips. Cover the surface with plastic wrap, and freeze for at least 6 hours.
Uncover and invert bowl onto a serving platter; remove plastic wrap. Combine cocoa and cinnamon, and sift over bombe. Let stand at room temperature 15 minutes before serving. Cut into wedges, using a sharp knife dipped in hot water.