Cook sausage in a large skillet over medium-high heat until crumbled and browned; place into a large Dutch oven. Sear venison cubes until well browned; add to sausage. Add ground venison, and cook until crumbly and no longer pink; place into Dutch oven.
Heat olive oil in the skillet over medium-high heat. Stir in the mushrooms, and cook until soft, about 2 minutes. Stir in onion and garlic, cook until the onion is translucent, about 2 minutes. Add the green and red peppers, red chile pepper, and jalapeno; cook until softened, then add to Dutch oven.
Stir in tomato paste, tomato sauce, black beans, diced tomatoes, and water. Season with chili powder, paprika, cayenne, and oregano. Bring to a simmer over medium-high heat, then reduce heat to medium-low, cover, and simmer until the venison pieces are tender, about 2 hours.
Season to taste with salt and pepper, and stir in parsley before serving. To serve, sprinkle with shredded Cheddar cheese.
