1. Place potato in a saucepan; cover with water. Bring to a boil. Reduce heat, and simmer 10 minutes. Add broccoli; cook an additional 7 minutes or until potato and broccoli are tender.
2. Drain potato and broccoli; place in a small bowl. Add cheese, and let stand until cheese melts.
3. For a chunkier texture, mash potato mixture with a potato masher to desired consistency. For a smoother texture, place potato mixture in a food processor, and process until desired consistency.