Soften the vegetables: Heat the olive oil in a large Dutch oven or heavy pot over medium heat. Add the onion and bell pepper and cook for 5 minutes, stirring now and then, until they soften and the onion turns translucent.

Brown the turkey: Add the ground turkey and break it apart with a wooden spoon. Cook for 7-8 minutes, until no pink remains and the meat reaches an internal temperature of 165°F on an instant-read thermometer. Ground turkey is poultry, so 165°F is the number here, not the 160°F you'd use for ground beef.

Bloom the spices: Stir in the garlic, chili powder, cumin, oregano, smoked paprika, salt, black pepper, and cayenne if using. Cook for 1 minute, stirring constantly, until the spices smell toasty and cling to the meat.

Add the tomatoes and beans: Pour in the crushed tomatoes, tomato sauce, and chicken broth, then stir in the kidney beans and black beans. Scrape the bottom of the pot to lift anything stuck on.

Simmer uncovered: Bring it to a gentle bubble, drop the heat to low, and simmer uncovered for 30 minutes, stirring every 10 minutes or so. It's ready when the chili thickens enough to mound on a spoon instead of running flat.

Taste and serve: Taste and add salt if it needs it. Ladle into bowls and top with the shredded cheddar, sour cream, and sliced green onions.