Gather all ingredients. Pour oil to a depth of 2 inches in a large Dutch oven; heat oil over medium-high to 360 degrees F (182 degrees C). Preheat oven to 200 degrees F (93 degrees C). Set a wire rack inside a large rimmed baking sheet; set aside.

While oil heats, pat fillets dry with paper towels, and sprinkle evenly with 1/2 teaspoon of the salt. Whisk together egg, mayonnaise, Dijon mustard, corn starch, flour, paprika, and remaining 1/2 teaspoon salt in a medium shallow bowl until combined. Place panko in another shallow bowl. Working with one fillet at a time, dip into egg mixture, flipping to coat all sides and letting excess drip off. Place in bowl with panko, and coat all sides. Place on a large plate; repeat with remaining fillets.

Gently add 2 fillets to hot oil; fry, gently stirring and flipping fillets in oil occasionally, until golden brown and crispy, 3 to 5 minutes. Remove fillets from oil using a slotted spoon, and place on prepared wire rack. Place in preheated oven to keep warm while repeating frying process with remaining 2 fillets.

Working with 2 buns at a time, place bottom buns on a large microwavable plate; top each bun with 1 cheese slice. Lightly sprinkle a small paper towel with water, and place in small microwavable bowl with bottom buns. Cover plate with an inverted microwavable glass bowl. Microwave on HIGH until buns are steamy and cheese is melted, 15 to 20 seconds. Carefully remove buns from plate; place top buns on the same plate and microwave on HIGH for 10 to 15 seconds.

Immediately top bottom buns with a fish fillet and drizzle 2 tablespoons McDonald’s Tartar Sauce on top. Cover with top buns and serve immediately with shoestring fries. Repeat with remaining buns and fish fillets.