Heat a large skillet over medium-high heat. If using lean ground beef, drizzle in olive oil. Add ground beef and cook for 4–5 minutes until browned.

Add finely diced yellow onion to the skillet and sauté for 2–3 minutes until soft. Then, add minced garlic and stir for 30 seconds until fragrant.

Reduce heat to medium and add ketchup, tomato paste, Worcestershire sauce, yellow mustard, brown sugar, and smoked paprika. Mix well, season with salt and pepper, and let simmer for 5–7 minutes until thickened.

Toast the brioche or hamburger buns in a skillet or toaster. Optionally, spread mayonnaise or butter inside for added flavor.

Assemble the sandwiches by placing lettuce on the bottom bun, adding the meat mixture, and sprinkling cheddar cheese on top. Cap with the top bun and serve hot.