Heat the oil in a large pot or Dutch oven to medium heat. (If using bacon, cook it down for 3 minutes to render the fat).
Season the chopped stew beef with salt and pepper. Add to the pot and brown the meat on each side, about 5 minutes. Remove and set aside. (NOTE: Browning this way isn’t necessarily traditional, but it works for so many other recipes and I love the way it seals in the juices of the meat, prepping it for low and slow cooking).
Add the onion and cook 5-6 minutes to soften.
Reduce the heat (or pull the pot away from the burner) and stir in the paprika. Stir it off heat for 1 minute to let the paprika bloom. Removing it from the heat will avoid burning the paprika, which turns it bitter.
Return the pot to medium heat and add the reserved beef, bell peppers, garlic, tomatoes, beef broth (or water), and bay leaves (and caraway seeds, if using). Bring to a boil, then reduce heat. Simmer for 1.5 hours. The liquid should reduce a bit.
Add the potatoes and carrots. Add more water or beef stock for a soupier goulash (1-2 cups, as desired). Cover and simmer another 30 minutes, or until the vegetables are tender and the meat is done to your liking.
Adjust for salt and pepper, and serve.