Heat oil in a large pot over medium heat. Cook chicken breasts in hot oil until well browned on all sides. Remove and set aside.

Cook and stir onion and garlic in drippings in the same pot until onions are translucent. Pour in chicken broth.

Whisk together 2 cups water and masa harina in a medium bowl until well blended; pour into the pot. Stir in Cheddar cheese, enchilada sauce, remaining 1 cup water, salt, chili powder, and cumin. Bring to a boil.

Shred cooked chicken and add it to the pot. Reduce heat and simmer until thickened, 30 to 40 minutes.