Add the olive oil to a large Dutch oven over medium-high heat. Once hot, add the onions and peppers and saute until soft, about 4 minutes. Add the garlic and saute until just fragrant. Stir in the beef and sausage, breaking it up with the back of a wooden spoon, and cook until browned, about 6 minutes.
Drain the beef mixture through a colander. Add it back to the Dutch oven and stir in the chili powder, cumin and oregano. Cook for about 2 minutes. Stir the tomato paste into the beef mixture; this will "toast" it and give the chili more flavor. Add the beer and stir up any browned bits on the bottom of the pan. Bring to a simmer, and then add the diced tomatoes and beans. Simmer on medium-low for 2 hours, stirring on occasion to keep the bottom from sticking.
Top with shredded cheese, sour cream and chopped green onions before serving.
From Food Network Kitchens; after further testing and to ensure the best results this recipe has been altered from what was in the actual episode.