Heat the vegetable oil in a large pot over medium-high heat. Add the tomato paste, chili powder and cumin and cook, stirring, until the mixture darkens, about 1 minute. Add 1/2 cup water, the bell pepper, scallion whites and 1 teaspoon salt. Cook, stirring, until the bell pepper is crisp-tender, about 4 minutes. Add the turkey and cook, breaking up the meat with a wooden spoon, until cooked through, about 4 minutes.
Stir the tomatoes, chicken broth, beans and crushed tortilla chips into the pot; bring to a simmer. Partially cover and cook, stirring occasionally, until thickened, 10 to 12 minutes. Stir in all but a few tablespoons of the scallion greens and season with salt. Top with more crushed tortilla chips, sour cream, cheddar and the remaining scallion greens.