Sauté onion in hot oil in a 10-inch cast-iron skillet over medium-high heat 3 to 4 minutes or until tender. Stir in beans and next 8 ingredients. Bring to a boil; reduce heat and simmer, uncovered, 15 minutes.
Combine baking mix, egg, and milk in a medium bowl, stirring until smooth. Fold in 1/2 cup cheese and 1/4 cup cilantro; pour over simmering chicken mixture.
Bake at 400° for 20 minutes or until a wooden pick inserted in topping comes out clean. Sprinkle with remaining 1/2 cup cheese and remaining 1/4 cup cilantro. Sprinkle avocado slices with lime juice, and arrange over cobbler. Serve with sour cream.