Heat olive oil in a large pot or Dutch oven over medium-high heat.
Add ground turkey and cook until browned, breaking it into small crumbles with a spatula.
Add diced onion and bell pepper to the pot; cook for 5 minutes until softened.
Stir in minced garlic, chili powder, cumin, paprika, oregano, and cayenne; cook for 1 minute until fragrant.
Stir in tomato paste until well incorporated with the meat and vegetables.
Add crushed tomatoes, black beans, kidney beans, and chicken broth; stir to combine.
Bring the mixture to a boil, then reduce heat to low and simmer, partially covered, for 30 to 40 minutes.
Season with salt and pepper to taste before serving.