Heat the olive oil in a large skillet over medium-high heat. Add the turkey and cook, breaking it into small pieces, 6 to 8 minutes, until no longer pink. Transfer to a plate.
Add the onion and bell pepper to the skillet and cook 4 minutes, until softened. Stir in the garlic, chili powder and salt and cook 30 seconds, until fragrant.
Stir in the tomato sauce, tomato paste, Worcestershire sauce and brown sugar, if using. Return the turkey and its juices to the skillet.
Simmer 8 to 10 minutes, stirring often, until the sauce thickens and coats the meat. Taste and add more salt if needed.
Spoon the mixture onto the toasted buns and serve warm.
