How to Make It
Preheat broiler on low with oven rack 6 inches from heat source. Place kale pieces on a large rimmed baking sheet. Drizzle with 2 tablespoons of the olive oil; toss to coat. Arrange in a single layer; broil until kale is slightly crisp and browned in spots, about 8 minutes.
Heat remaining 2 tablespoons oil in a medium Dutch oven over medium. Add sweet potato, onion, and garlic; cook, stirring occasionally, until onions are softened, about 7 minutes. Add turkey, increase heat to high, and cook, stirring often, until turkey is no longer pink, 5 to 7 minutes.
Stir in tomato paste, chili powder, ancho chile powder, cumin, and oregano; cook, stirring constantly, until fragrant, about 1 minute. Stir in chicken stock, tomato sauce, diced tomatoes, black beans, salt, vinegar, and kale. Bring to a boil over high. Reduce heat to medium, and simmer, stirring occasionally, until sweet potatoes are tender, about 20 minutes. Divide chili among 6 bowls; top each with a dollop of sour cream, and garnish with cilantro and jalapeños.