Heat olive oil in a large non-stick skillet over medium-high heat.
Add the diced onion and bell pepper to the skillet and sauté for 5 minutes until vegetables are softened and translucent.
Add the ground turkey to the skillet, breaking it into small crumbles with a wooden spoon, and cook until browned and no longer pink.
Stir in the minced garlic and cook for 60 seconds until fragrant.
Whisk together tomato sauce, tomato paste, apple cider vinegar, mustard, maple syrup, chili powder, smoked paprika, salt, and pepper in a small bowl.
Pour the sauce mixture over the turkey and vegetables; stir thoroughly to combine.
Reduce heat to low and simmer for 10 minutes, stirring occasionally, until the sauce has thickened to the desired consistency.
Toast the whole wheat buns and divide the mixture evenly among the four buns to serve.