Bring a large pot of salted water to a boil. Meanwhile, heat the olive oil in a large nonstick skillet over medium heat. Add the scallion whites and garlic and cook, stirring, until soft, 1 to 2 minutes. Add the tomato paste and chili powder and cook, stirring frequently, until the mixture is brick red, 2 to 3 minutes. Add the turkey and stir, breaking up the meat, until almost cooked through, about 4 minutes. Add the chicken broth, beans and ketchup; bring to a simmer and cook until the chili is slightly thickened but still soupy, 12 to 15 minutes. Stir in the scallion greens and hot sauce.
Meanwhile, add the pasta to the boiling water and cook as the label directs, then drain. Divide among bowls and top with the chili, cheese and sour cream.