Combine cream cheese, 1 cup shredded cheddar, and chilies in a medium mixing bowl, and mix until thoroughly combined. Pour the rest of the shredded cheddar cheese into a shallow bowl or onto a plate. Form the cheese into a ball, roll in the shredded cheese until fully coated, and wrap tightly in plastic wrap.
Wrap twine or place rubber bands around the cheeseball 4 times at intervals to create indentations as in a pumpkin.
Refrigerate until firm, about 2 hours. Remove twine and plastic wrap. Cut the stem from the bell pepper and insert in the top of the pumpkin cheeseball. Slice the pepper and serve with the cheeseball along with crackers and other crudités.