Heat 2 tbsp olive oil in a large skillet over medium-high heat. Once it shimmers, add your diced onion and red bell pepper.
Let them sit for about 3 minutes without stirring — this creates caramelization and deepens the flavor. Stir and cook for another 2 minutes until they're soft and slightly browned.
Add the 1 lb ground beef to the skillet, breaking it apart with a wooden spoon. Cook for about 4 minutes, stirring occasionally, until the meat is no longer pink and has some light brown color.
Push the meat mixture to the side of the skillet. Add 2 tbsp tomato paste to the empty space and let it sit for about 1 minute. This toasts the tomato paste and removes that raw flavor. Stir it into the meat.
Pour in 1/2 cup ketchup, 2 tbsp brown sugar, 1 tbsp mustard, 1/4 cup water, 1/4 tsp black pepper, and 1 tsp smoked paprika. Stir everything together until combined.
Reduce heat to medium-low and let it simmer for about 5 minutes. You want the sauce to thicken slightly and the flavors to meld together. It should look like a thick, saucy filling, not watery.
Taste it and adjust seasonings if needed. Need more sweetness? Add another tablespoon of brown sugar. Want more tang? Add a splash more mustard.
Toast your hamburger buns lightly if you want them to hold up better against the sauce. It's optional but honestly makes a difference.
Spoon the filling onto each bun and serve immediately. The filling will stay warm for about 10 minutes.