Sauté the onions. Heat a large pot or Dutch oven over medium heat. Add the butter and 1 tablespoon olive oil and cook the onions until soft, approximately 6-8 minutes. Stir often.
Cook the paprika. Reduce heat to low (or completely remove from heat) and sprinkle the onions with paprika. Mix well to combine and cook on LOW as this will bring out the flavors of the paprika rather than turn it bitter.
Cook the beef and garlic. Increase heat to medium-high. Immediately add the beef, mixing well. Cook the beef for 5 minutes, or until no longer pink in the middle (cooking times will vary depending on the size of beef chunks). Add the garlic and mix well to combine. Cook, stirring continuously, for approximately 1 minute.
Add the carrots and bell peppers. Cook for 3-4 minutes, stirring often.
Work in the tomatoes and make a broth. Push the beef and vegetables to the side of the pot. Add the tomato paste and 1 tablespoon of olive oil to the other side. Cook the tomato paste, whisking continuously, until a brown fond (the browned bits) forms on the bottom of the pot. This will take approximately 1-2 minutes. Still stirring, add the chopped tomatoes, beef broth, salt and pepper, and bay leaf. Scrape the brown bits from the bottom of the pot and bring to a boil.
Simmer. Reduce heat to low and simmer, covered, for approximately 45-60 minutes. Serve with egg noodles, fresh bread, and buttered bread, if desired.