In a large skillet, heat the olive oil over medium high heat. Add the onion and red pepper and cook for 3 minutes, stirring occasionally. Add the garlic and cook for 2 more minutes or until vegetables are tender.
Add the ground beef or turkey and season with salt and pepper. Cook until browned, using a wooden spoon to break up the beef or turkey. Stir in the tomato paste, brown sugar, smoked paprika, and chili powder.
Stir in the tomato sauce, apple cider vinegar, mustard, and Worcestershire sauce. Reduce heat to low and let simmer for 10 to 15 minutes, stirring often.
Taste and adjust seasonings if necessary. You can add more salt and pepper, more brown sugar if you want it a little sweeter, or more chili powder or crushed red pepper flakes, if you want it spicier.
To serve, spoon mixture onto toasted buns. Serve immediately.
Store leftover sloppy joe mixture in an airtight container in the fridge for up to 4 days. Freeze the mixture for up to 3 months. Thaw and reheat.