Combine Cheddar cheese and next 4 ingredients in a bowl until blended. Cover and chill 4 hours or until mixture is firm enough to be shaped.
Shape mixture into a ball to resemble a pumpkin. Smooth entire outer surface with a frosting spatula or table knife. Make vertical grooves in ball, if desired, using fingertips.
Cut florets from broccoli stalk, and reserve for another use. Cut stalk to resemble a pumpkin stem, and press into top of cheese ball. Serve cheese ball with apple wedges.
Note: To make ahead, wrap cheese ball in plastic wrap without stalk, and store in refrigerator up to 2 days. Attach stalk before serving.