Step 1: Dice the boneless, skinless chicken thighs into 1-inch pieces. Season generously with salt, black pepper, and a pinch of cumin.
Step 2: Dice the onion, mince the garlic, and chop the roasted green chiles (if using fresh, roast, peel, and seed them first).
Step 3: In a large Dutch oven or heavy-bottomed pot, heat 1 tablespoon of olive oil over medium-high heat. Add the seasoned chicken pieces and sear until lightly browned on all sides. Remove the chicken and set aside.
Step 4: Add another tablespoon of olive oil if needed. Lower the heat to medium and add the diced onion. Sauté for 5-7 minutes until softened and translucent.
Step 5: Stir in the minced garlic and cook for another minute until fragrant, being careful not to burn it.
Step 6: Add the ground cumin, dried oregano, and cayenne pepper (if using) to the pot. Cook for 30 seconds, stirring constantly, until the spices are fragrant.
Step 7: Pour in the chicken broth, scraping the bottom of the pot with a wooden spoon to deglaze and incorporate all those flavorful browned bits.
Step 8: Stir in the chopped green chiles and diced tomatoes. Bring the mixture to a simmer.
Step 9: Return the seared chicken to the pot. Add the drained and rinsed hominy.
Step 10: Reduce the heat to low, cover the pot, and let the stew simmer gently for at least 45 minutes to 1 hour, or until the chicken is incredibly tender and the flavors have melded beautifully. Stir occasionally.
Step 11: Taste and adjust seasonings as needed. You might want to add more salt, pepper, or a squeeze of lime juice for brightness.
Step 12: Ladle the hearty green chili stew into bowls. Garnish with fresh cilantro, a dollop of sour cream or Greek yogurt, shredded cheese, diced avocado, and a lime wedge. Serve warm.