Heat the oil in a large skillet over medium-high heat. Add ground beef. Crumble with a cooking spoon and cook until browned and cooked through, about 7 to 8 minutes. Transfer the browned beef to a plate; set aside.
Return the pan to medium-high heat. Add the onion, pepper, and garlic. Cook until
softened, about 6 to 8 minutes. Add the chili powder, paprika, and salt. Cook until fragrant, about 1 minute.
Add the tomato sauce, tomato paste, brown sugar, and mustard. Stir to combine. Return the ground beef to the pan. Stir to incorporate.
Simmer the sauce, stirring often, until thickened, about 15 minutes.
Taste and add salt and pepper as needed. Spoon onto the toasted buns.