Rub 1 tablespoon vegetable oil over chicken breast. Cook chicken in a medium saucepan over medium heat until meat is no longer pink and juices run clear, about 5 minutes per side. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Remove from heat and set aside.

Heat remaining 1 tablespoon vegetable oil in the saucepan over medium heat. Stir in green onion and bell pepper. Cook and stir until tender, about 5 minutes.

Dice chicken and mix into the pan with green onion and bell pepper. Mix in corn, black beans, spinach, jalapeño peppers, parsley, cumin, chili powder, salt, and cayenne pepper. Cook and stir until well blended and tender, 5 minutes. Remove from heat and stir in Monterey Jack cheese so that it melts.

Wrap tortillas with a clean, lightly moist cloth. Microwave on high until hot and pliable, about 1 minute.

Spoon even amounts of the mixture into each tortilla. Fold ends of tortillas, then roll tightly around the mixture. Secure with toothpicks. Arrange in a medium dish, cover with plastic, and place in the freezer. Freeze for at least 4 hours.

Heat oil in a large, deep skillet for deep-frying to 375 degrees F (190 degrees C). Deep-fry frozen, stuffed tortillas until dark golden brown, about 10 minutes each. Drain on paper towels before serving.