In a medium pot over medium heat, add the oil and garlic and cook until just beginning to turn light golden, about 3 minutes, stirring often. Add the tomato paste now (if using) and let it cook for about 2 minutes, stirring often. Stir in the spices for about 30 seconds, followed by the water and salt.
Nestle the chicken into the liquid and gently stir to get some of that liquid onto the chicken. Bring the liquid to a simmer, then cover and simmer gently for about 15 minutes, flipping the chicken halfway through. This may take shorter or longer depending on the thickness of your breast. The best way to know if it’s done is to check the internal temp (you want between 155-160F).
Once cooked through, transfer chicken breasts to a cutting board to rest. Turn the heat back on the pot and simmer rapidly for about 5-8 minutes or until the liquid has reduced significantly (see video).
Use two forks to shred up the chicken (or add them whole back to the pot and use an electric hand mixer to shred it up). Stir the shredded chicken to coat in the sauce, making sure to scrape up all the bits of sauce stuck to the pot.
If making the cilantro sauce, add all ingredients to a high-speed blender and blend on high until smooth.
You can turn this into a taco, taco bowl, taco salad, or quesadilla. Or just add the chicken to any salad or bowl.