Combine flour, garlic, cumin, oregano and black pepper in a large resealable plastic bag. Place chicken in bag and gently toss with flour mixture to completely coat.
Heat oil in large nonstick skillet over medium high heat; add chicken to skillet. Sauté chicken until lightly browned about 6 to 8 minutes.
Remove any floating beans; drain water and place beans in slow cooker. Add vegetables, chicken broth, 1/2 cup salsa verde and water to the slow cooker.
Place chicken in slow cooker; stir to combine ingredients.
Cook on HIGH for 4 to 6 hours or LOW for 7 to 9 hours or until beans are tender. Stir in remaining salsa verde, evaporated milk, cheese and cilantro. Serve with sliced jalapenos and additional cilantro, if desired.