Combine Cheddar cheese, cream cheeses, 2 teaspoons paprika, and red pepper in a big bowl. Beat at medium speed with an electric mixer until blended. Cover with plastic wrap, and chill at least 1 hour.
Shape cheese mixture into a ball, and place on a flat serving plate. Make vertical grooves in ball using the handle of a wooden spoon to resemble a pumpkin, and dust grooves with paprika, if you'd like. Cover cheese ball with plastic wrap, and refrigerate up to 5 days. Cut florets from broccoli; save them to eat later. Trim small leaves from broccoli stalk. Cut stalk to look like a pumpkin stem; press into top of cheese ball along with small leaves from broccoli. Serve with apple wedges or crackers.