Place the drained tuna fish and the tartar sauce in a medium-sized bowl and stir well until combined.
Cut the bagels in half and toast until your desired doneness.
Place the bagels onto a baking sheet (cut side up) and place the cheddar cheese slices onto each bagel half.
Add a layer of prepared tuna salad to each bagel with cheese and sprinkle each with the shredded Parmesan cheese.
Place in the preheated oven for 3-5 minutes, or until the cheese has melted.
Serve hot.
Notes
The prepared tuna salad may be kept in the refrigerator for up to 5 days in an airtight container.Tuna in water may be substituted for tuna in oil if desired.For best consistency, always drain the tuna well before adding additional ingredients.