For the Tuna Melts:
1 Make the pickled veggies: Peel and slice the carrot in half down its length and then into thin half-coins. Slice the radishes in half and then slice into half-coins as well. Do the same with the pickle.
Stir the vegetables together with 3 tablespoons of pickle juice to coat. Set aside for a few minutes while you make the tuna melt muffins. Taste, and add more pickle juice if needed.
2 Preheat oven to 400°F.
3 Make the tuna mixture: In a medium bowl, stir together minced celery, onion, red pepper, salt, pepper, and tuna. Fold in the mayo last.
4 Prep the tuna melts: Spread out English muffin halves on a baking sheet. Add half a slice of Swiss cheese to the bottom of each muffin. Top each muffin with about two tablespoons of tuna salad mix. Top with second half of cheese.
5 Bake: Bake the tuna melts for 12 to 15 minutes until muffins are browned around the edges and the cheese is melted.
6 Serve: Serve while warm with pickled veggies on the side (optional).