Heat oil in a 6-quart pot over medium-high heat. Cook turkey and onion for 8 minutes, breaking up the meat, until the turkey reaches 165°F.
Stir in cumin, chili powder and salt for 30 seconds. Add salsa verde and broth and bring to a simmer.
Whisk refried beans into the liquid until evenly dispersed, then fold in whole pinto beans and corn.
Simmer uncovered for 12 to 15 minutes, stirring from the bottom, until corn is hot and the soup is lightly thickened.
Stir in lime juice. Divide among 6 bowls and top evenly with Monterey Jack and crushed tortilla chips just before eating.