Make the sauce: in a bowl whisk together 3/4 cup mayonnaise, 1 tablespoon ketchup, and 1 teaspoon Dijon mustard until smooth.
Stir in 1 teaspoon dill relish (or chopped pickles), 1/2 teaspoon Worcestershire sauce, 1/2 teaspoon garlic powder, 1/2 teaspoon onion powder, and 1/2 teaspoon paprika; season with salt and pepper to taste.
Cover the sauce and refrigerate for at least 30 minutes to let the flavors meld while you prepare the chicken.
Prepare the breading: in a shallow dish combine 1 cup all-purpose flour, 1 tablespoon paprika, 1 teaspoon garlic powder, 1 teaspoon onion powder, 1 teaspoon salt, and 1/2 teaspoon black pepper; mix well.
In a second shallow dish whisk together 1 cup buttermilk and 2 eggs until blended.
Trim each chicken breast cutlet to fit the buns if needed, then dip a cutlet into the buttermilk mixture, allowing excess to drip off, and dredge it thoroughly in the flour mixture; shake off excess.
Heat enough vegetable oil in a large skillet over medium-high heat so it reaches about 350°F (use a thermometer to check).
Carefully add the breaded chicken cutlets to the hot oil and fry 4–5 minutes per side, or until golden brown and cooked through (internal temperature 165°F).
Transfer the fried cutlets to a wire rack or paper towels to drain briefly.
Toast the hamburger buns and spread about 1 tablespoon BK Royal Sauce or mayonnaise on the bottom half of each bun.
Place a fried chicken cutlet on each bun bottom, top with a tomato slice and two lettuce leaves, then place the bun top and serve immediately.