Finely chop or grind the smoked sausage, then combine it with the ground pork in a large bowl.
Mince the onion and garlic, then add them to the meat mixture. Crack in the egg, add the breadcrumbs, salt, black pepper, and Hungarian sweet paprika. Mix everything thoroughly until well combined.
Form the mixture into four equal-sized patties. Flatten them slightly to prevent them from shrinking too much during cooking.
Heat a skillet or grill to medium-high heat, then cook the patties in a little oil for 4-5 minutes per side, or until they are nicely browned and cooked through.
In the last minute of cooking, place a slice of cheddar cheese on each patty and cover the skillet to allow the cheese to melt.
Halve the hamburger buns and lightly toast the cut sides in a dry skillet.
Spread a little mayonnaise and Dijon mustard on the bottom bun, top with lettuce, then the cheese-topped patty. Add sliced tomatoes, and finally, the top bun.
Serve the prepared burger immediately, with fries or other side dishes.
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