Pre-heat oven to 350 degrees and place red pepper halves in a large glass baking dish; set aside.
Heat a large sauté pan over medium heat. Spray with cooking spray and add diced onion and carrot. Cook onion until softened, 3-4 minutes.
Add grated garlic to the pan and heat 30 seconds before adding ground bison. Bump heat up to medium-high and brown the bison while breaking it down with a wooden spoon. While bison is browning, throw in the mushrooms and spices (oregano through chili flakes.)
Once mushrooms have lost most of their moisture and bison is nicely browned and starting to form a crust (after about 10 minutes), stir in the tomato paste. Use wooden spoon to help incorporate paste into the meat mixture.
Pour in the tomato sauce and cooked rice. Stir to combine and cook for an additional 2-3 minutes until mixture is warmed through. Check for seasoning and adjust accordingly before removing pan from the heat.
Fill each pepper half with a heaping half cup of the bison and rice mixture. If there is leftover mixture simply add it to the pan around the peppers.
Sprinkle a tablespoon of shredded parmesan on top of each stuffed pepper. Cover pan with foil and bake until peppers are soft, about 30-40 minutes.
Optional: Once peppers are cooked, remove foil from the pan and broil peppers for 30-60 seconds to brown the cheese and form a bubbly crust on top.