In a large pot over medium-high heat, sauté onion and garlic with olive oil until softened. Add the chicken and spices and cook for 5 minutes until fragrant.
Once the chicken is slightly browned, top up with enough water to cover the chicken (at least 6 cups), and bring to a simmer. Remove all of the froth and extra oil that rises to the top.
Simmer on medium-low heat for about 1 hour or more until very tender. Meanwhile, prep all the toppings and place them in small bowls to serve later.
Remove chicken from the stock and shred it, discarding the bones and skin, then add it back to the stock.
Add the hominy with some of the liquid it comes in, and cook covered for another 15-20 minutes.
Serve the soup nice and hot with all the toppings on the side. Making it perfect for everyone to customize their own bowls.