Add 1 tablespoon oil to a large pot over medium heat. Add chicken breasts to pot and brown for 4-5 minutes per side, or until they are no longer pink. Remove chicken from pot and set aside. Add onions to the remaining oil in the pot (if there isn't much left, add a bit more), and saute over medium heat for about 3 minutes, or until onions begin to become translucent. Add garlic and saute for 30 seconds. Add chicken broth. In a medium bowl or measuring cup, add 2 cups of water. Add the masa harina gradually, whisking constantly. (This helps avoid grainy-ness.) Add masa mixture to pot with onions, garlic and broth. Add remaining water, enchilada sauce, Velveeta, and spices to the pot and bring mixture to a boil. Shred the chicken into small, bite-size pieces and add it to the pot. Reduce heat to low and simmer soup for 30-40 minutes or until thick. Serve soup garnished with shredded cheddar cheese, crumbled corn tortilla chips, avocado, and Pico de Gallo.