Heat the oil in a large Dutch oven over medium-high heat. Add the turkey and cook, breaking it up with a spoon, for 5 to 6 minutes, until no longer pink.
Add the onion and bell pepper and cook for 5 minutes, stirring, until softened. Stir in the garlic, chili powder and cumin and cook for 30 seconds, until fragrant.
Add the tomatoes and their juices, both beans, the broth and the salt. Bring to a boil, then reduce the heat to low.
Simmer uncovered for 20 to 25 minutes, stirring occasionally, until slightly thickened. Taste and add more salt if needed, then serve hot.