1. Bring first 6 ingredients to a boil in a small saucepan. Stir in shredded chicken and green onions.
2. Combine beans and salsa. Spoon 1/4 cup bean mixture and 1/2 cup chicken mixture down center of each tortilla; sprinkle with 2 tablespoons cheese. Roll up.
3. Heat a large skillet over medium-high heat. Coat pan with cooking spray. Add 2 burritos. Place a cast-iron or other heavy skillet on top of burritos, and cook for 3 minutes on each side. Remove from pan, and repeat procedure with the remaining 2 burritos.