In a large pot or Dutch oven over medium heat, heat oil. Add sausage and cook, stirring occasionally, until browned and cooked through, about 6 minutes. Add onion, bell pepper, garlic, chili powder, cayenne, and oregano; season with salt. Cook, stirring, until tender, 6 to 7 minutes. Add tomato paste and cook, stirring, until slightly darkened, about 1 minute.
Add broth, beans, and diced tomatoes and bring to a boil. Reduce heat to medium-low, bring to a simmer, and add kale; season with salt. Simmer, stirring occasionally, until chili is thickened, about 30 minutes.
