01 - Set oven to 375°F. Ensure oven rack is centered.
02 - Arrange hollowed bell peppers upright in a baking dish. Pour 1/4 inch of water into the bottom to support even cooking.
03 - In a large skillet over medium heat, break up ground beef and cook until no longer pink, around 5 minutes. Remove and discard excess fat if present.
04 - Add chopped onion, grated carrot, and minced garlic to the skillet. Sauté until vegetables begin to soften, about 3 minutes.
05 - Incorporate tomato sauce, tomato paste, Worcestershire sauce, brown sugar, smoked paprika, salt, black pepper, and optional red pepper flakes. Simmer on medium-low for 5 to 7 minutes until thickened and fragrant.
06 - Divide the Sloppy Joe mixture among the bell peppers, filling each cavity evenly.
07 - Cover the baking dish tightly with foil and bake for 25 minutes.
08 - Uncover dish, sprinkle the top of each stuffed pepper with shredded cheddar. Bake uncovered for an additional 10 minutes, until cheese is melted and bubbly and peppers are fork-tender.
09 - Remove from oven and sprinkle with chopped parsley, if desired. Serve immediately.