Preheat oven to 425 degrees F. Halve the peppers and remove the seeds, stems and membranes. In a 9x13 inch baking dish, toss the bell peppers with 1 tablespoon of olive oil and 1/2 teaspoon of salt. Place the bell peppers cut side up and set aside.
In a large skillet or frying pan, heat the remaining olive oil over medium-high heat. Add the turkey to the pan and break up with a spoon. Cook until the turkey is no longer pink, about 4 minutes. Add the onions and carrots, cook for another 4-5 minutes until softened. Add garlic and cook for an additional minute.
Season the turkey meat with 1/2 teaspoon of salt, pepper, chili powder, paprika, ketchup, Dijon mustard, light brown sugar, Worcestershire sauce and parsley. Stir and add 1/2 cup of water. Bring to a simmer and let the meat and seasonings cook together until thickened, about 10 minutes.
Evenly distrubute the Sloppy Joe filling into the pepper halves by spooning the mixture into the peppers. Sprinkle the filled peppers with shredded cheddar cheese. Pour 1/4 cup of water in the bottom of the baking dish and cover with foil.
Bake until peppers are tender and soften, about 30 minutes. Remove the foil and bake for another 15 minutes until the cheese is bubbly and the filling has browned. Garnish with parsley and serve. Enjoy!