Chuy's Green Chile Stew

Source: Chuy's - San Antonio, Texas

2 cups (approximately 6 to 8 chiles) fresh Sandia
    green chiles *
1 (3- to 4-pound) whole chicken, cut into 8 pieces
1 to 2 tablespoons vegetable oil, or as needed
6 cups onions, sliced 1/2-inch thick
4 cups carrots, diced into 1-inch cubes
6 cloves garlic, minced
4 cups tomatillos, husks removed, rinsed and quartered
4 cups Roma tomatoes, quartered
1 tablespoon salt
1 tablespoon pepper
10 cups chicken broth
6 cups new potatoes, cut into 1-inch cubes
1/2 cup chopped cilantro
1 cup diced green onions
Flour tortillas for serving

* You can substitute a mix of New Mexican Anaheim and poblano chiles if Sandia  chiles are unavailable.

Broil green chiles in the oven 2 to 3 inches from the heat or lay over open flame on grill, turning chiles as the skins blacken. Peel chiles and discard skins; dice chiles.

In a heavy-bottom pot, brown the chicken pieces over medium heat in vegetable oil, about 15 minutes.

Drain all but 1 tablespoon of drippings. Add onions, carrots and garlic; saut