In a large stockpot, heat oil over medium-high heat. Cook onion until tender and golden, 8 minutes. Add garlic and jalapeño and cook until fragrant, about 2 minutes more. Add tomato paste, chili powder, and cumin and cook, stirring, 1 minute more.
Add turkey and cook, stirring, until cooked through and golden, 5 to 7 minutes. Add black beans and canned tomatoes, stirring to combine, then add broth.
Increase heat to a simmer and let cook, 25 minutes.
Serve in bowls and garnish with sour cream, scallions, and cheddar cheese.