Heat a large nonstick skillet over medium-high heat and add the olive oil. When the oil shimmers, add the chopped onion and diced bell pepper; sauté until softened, about 4 minutes.
Push the vegetables to the side and add the ground turkey to the pan. Break it up with a spatula and cook, stirring occasionally, until mostly browned but still slightly moist, about 5 minutes.
Stir the garlic into the turkey mixture and cook for 30 seconds until fragrant. Season with 1/2 teaspoon salt, smoked paprika, and black pepper.
Pour in the tomato sauce, ketchup, Worcestershire sauce and maple syrup. Stir well to combine, scraping any browned bits from the bottom of the pan with the apple cider vinegar to deglaze.
Reduce the heat to medium-low and simmer the mixture, uncovered, stirring occasionally until thickened to a saucy but not runny consistency, about 8–10 minutes. Taste and adjust salt if needed.
Remove the skillet from the heat and let the filling rest for 3 minutes; this helps the sauce set and concentrates the flavors.
Toast the buns lightly if desired, then spoon the turkey mixture onto the bottom halves. Top each with shredded cheddar if using and cover with the bun tops. Serve warm.