Heat oil in a large skillet over medium-high heat. Add ground beef and break into crumbles. Cook 6 to 8 minutes, leaving it undisturbed for 30 to 45 seconds at a time, until no pink remains and the edges are browned. Drain excess fat, leaving about 1 tablespoon in the pan.
Add onion and bell pepper. Cook over medium heat for 4 to 5 minutes until onion is translucent and pepper has softened. Add garlic and cook 1 minute, stirring constantly, until fragrant.
Push the mixture to one side. Add tomato paste to the cleared space and cook 1 to 2 minutes, stirring, until it darkens to a deep brick-red. Stir the cooked paste through the entire mixture.
Add ketchup, Worcestershire sauce, brown sugar, yellow mustard, smoked paprika, salt, pepper, and water. Stir until fully combined.
Reduce heat to medium-low. Simmer uncovered for 8 to 10 minutes, stirring every 2 minutes, until the sauce is thick enough to hold a brief channel when a spoon is dragged across the pan bottom.
Toast buns cut-side down in a dry skillet for 1 to 2 minutes until golden. Spoon filling onto buns, add pickles if using, and serve immediately.
