Preheat the oven to 375°F (190°C).
In a large skillet over medium heat, melt the butter.
Add the chopped onion, celery, and mushrooms to the skillet and sauté until softened, about 5 minutes.
Add the minced garlic and cook for 1 minute until fragrant.
Pour in the heavy cream and chicken broth, stirring to combine.
Add the Dijon mustard, salt, black pepper, dried thyme, and paprika. Stir well and let the sauce simmer for 3-4 minutes until slightly thickened.
Add the drained tuna and thawed peas to the skillet and gently fold to combine with the sauce.
Remove the skillet from heat and stir in 1 cup of shredded cheddar cheese until melted and well incorporated.
Transfer the mixture to a 9×9-inch baking dish.
Sprinkle the remaining 1/2 cup cheddar cheese and the grated Parmesan cheese evenly over the top.
Bake in the preheated oven for 15-20 minutes, or until the cheese topping is melted and golden brown.
Remove from the oven and let cool for 5 minutes before serving.