Preheat oven to 350° F.
Remove stems from dried chilies, then cut or tear into pieces. Add to a small saucepan with 1 cup water. Bring to a simmer over medium heat, reduce heat to maintain simmer for 10 minutes. Remove from heat and allow to cool. Puree until smooth, and set aside.
Dice elk into very small pieces. Season well with salt and pepper, if desired. Heat 1 tbs oil in a large skillet over medium heat. Brown meat in batches, then set aside.
In a large Dutch oven, braising dish, or similar lidded pot that can go from the stove top to the oven, heat the remaining 1 tbs of oil over medium heat. Add the onions and cook until translucent, about 5 minutes. Stir in garlic and cook for another minute or two, until it becomes fragrant. Add diced bell pepper and jalapenos and cook until slightly softened, about 5 minutes more.
Add meat to the pan, along with both types of beans, diced tomatoes, seasonings, and the reserved chili pepper paste. Stir in the beef broth and bring to a simmer.
Cover pot and transfer to oven. Cook at 350°F for 1½ to 2 hours, or until meat is extremely tender and liquid has thickened.