Prep the peppers: Cut the tops off the peppers and remove the seeds. Keep the tops as lids for later and set everything aside.
Make the filling: In a large skillet over medium heat, sauté the onion and carrot until soft, about 5 minutes. Add the ground meat and cook until browned, about 8–10 minutes. Stir in the uncooked rice, salt, pepper, paprika, garlic powder, and fresh parsley. Mix until everything is well combined. The rice will cook inside the peppers as they bake.
Stuff the peppers: Fill each pepper with the meat and rice mixture, pressing lightly but not packing it too tightly since the rice will expand while baking. Place the pepper tops back on.
Prepare the sauce: Heat the oil in a small saucepan. Add the flour and whisk to form a roux. Stir in the paprika, then slowly pour in the tomato sauce and water or broth. Add the sugar, if using, and season with salt and pepper. Simmer for a few minutes until smooth.
Bake: Place the stuffed peppers upright in a baking dish. Pour the sauce over and around the peppers so they are mostly covered. Cover tightly with foil or a lid and bake at 390°F for 1 hour and 30 minutes, until the peppers are tender and the rice is fully cooked.
Optional finishing touch: Remove the foil and bake for another 5–10 minutes to lightly brown the tops.
Serve: Sprinkle with fresh parsley and serve hot with mashed potatoes, sour cream, and/or fresh bread.