Gather your ingredients. Preheat oven to 200° (F). Place a small cooling rack inside a large baking sheet. Set aside as you prepare the breading and cook the fish.
In one bowl, whisk three eggs, until well beaten. In another bowl, add plain breadcrumbs, salt, pepper, and ½ a teaspoon of Old Bay Seasoning. Mix to combine. In another bowl, place Panko crumbs and the other ½ teaspoon of Old Bay Seasoning and mix to combine.
In a large deep heavy skillet over medium-high heat, add 1-inch of oil. Heat the oil to 360°.
While the oil is heating, pat the fish dry. Dip the fish in the beaten egg and then dredge in the plain bread crumbs. Make sure the fish is well coated on all sides. Place the coated fish back into the beaten eggs and then into the Panko crumbs. Continue with each piece of fish.
Add two of the breaded fish fillets to the preheated oil. Cook for 3–5 minutes per side. Carefully flip the fish over and cook the other side until golden brown and flaky. Remove with a fish spatula and place on a paper towel-lined plate. Allow the fish to drain for 1–2 minutes. Place the fried fish on the cooling rack inside the baking sheet. Keep fish warm in the preheated oven until ready to assemble the sandwiches.
To assemble the sandwiches, split the brioche buns in half. On each half, place 1–2 tablespoons of tartar sauce (see the recipe below or use store-bought sauce). On the bottom half, place a ½ cup of shredded lettuce if desired. Top with one of the fish fillets and one slice of cheese. Place the top half of the bun on top of the cheese and fish. Serve immediately.