Saute the beef and peppers:

1. Into a large, heavy pot (Enameled Cast-iron is ideal), over high heat, heat 1 T olive oil. Salt and pepper, then brown the beef cubes, in batches, on all sides.  As they become browned, remove beef to a separate bowl.
2. If the beef leaves a lot of fat in the bottom of the pot, wipe out the pot, pouring out all but about 1 T. Add a tablespoon of olive oil, and returning heat to medium-high, saute the chopped bell peppers until tender, about 6 minutes. Remove peppers to the bowl with the beef cubes.

Make the chili base:

1. Keeping heat at Medium to Medium high, add another tablespoon of olive oil, if needed, and saute the chopped onion, stirring regularly, for about 8 minutes, until golden.  Add the garlic, cumin, chili powder, paprika and brown sugar. Stir and saute for 30-60 seconds, until very fragrant.  Add the chilies and continue to saute 3 minutes.  Chilies should be softened slightly at this point.
2. Pour in the tomatoes and beef broth. Stir, and bring to low boil.
3. Remove from heat. Using an immersion blender, making sure to not splatter the hot base, blend spicy base until the onions and chilis are no longer visible. Mixture will be thick but not silky smooth.
4. Spoon the beef cubes and peppers, along with any accumulated juices, into the chili base, and simmer for at least an hour, but up to 4 hours, adding extra broth or water if needed to thin the base. Salt and pepper to taste.  Add additional chili powder or cumin if desired.
5. 30 minutes prior to serving, add the drained and rinsed beans, again adjusting flavor with salt if needed.
6. Serve in bowls with sour cream, shredded cheese and a squeeze of lime, if desired.