In a medium bowl combine shredded sharp cheddar, shredded mozzarella, softened cream cheese, Dijon mustard and optional hot sauce. Mix until a uniform, slightly sticky mixture forms. Transfer the mixture to a small piping bag or plastic bag with a corner snipped (or divide into two equal portions and form two small flattened disks about 2 inches across). Chill in the refrigerator while you shape the patties so the filling firms slightly (10–15 minutes).

Beef Patties

Season and portion beef

Place ground beef in a bowl. Add kosher salt, black pepper and Worcestershire sauce. Gently mix with your hands until just combined — avoid overworking. Divide meat into two equal portions (about 8 oz each if using 1 lb total) and form each portion into a ball.

Shape stuffed patties

Flatten each ball into a 4-inch patty. Place the chilled cheese filling disk (or pipe about 2–3 tbs of filling) in the center of one patty, leaving a 1/2-inch border. Place the second patty over the first and press the edges together to seal completely. Gently reshape into a uniform round, about 3/4-inch thick. Ensure there are no gaps so cheese won't leak excessively during cooking.

Cook the patties

Heat a cast-iron skillet or griddle over medium-high heat and add vegetable oil, swirling to coat. When the oil is shimmering (about 3 minutes), add the patties. Cook undisturbed for 3–4 minutes to develop a deep brown crust. Flip and cook the second side 3–4 minutes more, covering the pan with a lid for the last 1–2 minutes to help melt the interior cheese. The internal temperature should reach 160°F (71°C) for well-done; if you prefer slightly less done, aim for 155°F with caution. Transfer patties to a plate and rest 3–4 minutes so juices redistribute and filling settles.

Toppings & Assembly

Prepare buns

While the patties rest, spread softened butter on the cut sides of the buns. Toast buttered buns on the same skillet or a separate pan over medium heat until golden brown, about 1–2 minutes per side.

Assemble the burgers

Spread about 1.5 tbs of burger sauce on the bottom bun. Place a lettuce leaf, then the rested Gooey Louie patty. Top with tomato slices, red onion, and pickles. Spoon remaining burger sauce on the top bun and close the burger. Sprinkle a light pinch of smoked paprika and flaky sea salt over the tomato or bun if using.

Serve

Serve immediately while the center is hot and gooey. Offer extra napkins and an optional side of fries or a simple salad.