1. Hard-cook egg: place egg in small saucepan, cover with cold water. Bring to a boil; reduce heat and simmer, covered, for 10 minutes. Drain and cool in cold water. Peel and chop.
2. In a bowl, combine dry mustard and mayonnaise.
3. Stir in onions, celery, chopped egg, and drained tuna. Toss lightly to mix.
4. Mix in half of shredded cheese.
5. Lay out split English muffins onto a baking pan. Spread 1/4 cup of tuna salad to the edge of each muffin.
6. Sprinkle the top with 1 tablespoon of remaining shredded cheese.
7. Bake at 350° for 5 minutes until cheese is melted.