Heat a skillet on the stovetop over medium heat.
Coat the tuna steaks with olive oil and season with sea salt.
Add the steaks to the skillet and cook for 3 to 4 minutes, until a slight crust forms on the bottom, then flip and cook for 3 to 4 minutes on the second side. Once cooked, transfer the tuna steaks to a cutting board and coarsely chop them into 1/2-inch pieces.
Preheat the oven to 350°F.
Bring a large pot of water to a boil. Cook the noodles according to the package instructions.
While the noodles are cooking, in a large Dutch oven or other oven-safe pot, melt the butter over medium heat. Add the onion, garlic, and mushrooms and cook, stirring, for 4-5 minutes, until the onion and mushrooms have reduced in size. Add the flour and stir to combine. Slowly whisk in the milk and broth until smooth.
Add the tuna, peas, salt, and pepper and bring to a low boil.
When the pasta is done cooking, drain it and add it to the pot. Stir gently to combine.
Top with the cheese and transfer the pot to the oven. Bake for 20 minutes, or until hot and bubbling. Remove from the oven, garnish with the parsley, and serve.