Heat the olive oil in a large heavy pot over medium-high. Add the ground beef in an even layer and leave it completely undisturbed for 4 minutes, until a brown crust forms on the bottom.
Now break the beef up and finish browning, about 4 more minutes. Drain off excess fat but leave about 2 tablespoons in the pot.
Add the onion and bell pepper and cook for 5 minutes. Stir in the garlic and cook 30 seconds more.
Add the chili powder, cumin, smoked paprika, and oregano. Stir constantly for 1 full minute — the spices should smell toasted, not raw.
Stir in the tomato paste and cook for another minute, until it darkens.
Pour in the crushed tomatoes and beef broth, scraping the bottom of the pot hard to lift every browned bit.
Add both cans of beans and the brown sugar. Bring to a boil, then reduce to a low simmer.
Simmer partially covered for 45 minutes, stirring occasionally, until thick enough to hold a spoon upright for a second.
Season with salt to taste and serve with shredded cheddar, sour cream, and green onions.