In a large pot, combine the chicken breasts and water. Bring to a boil over medium-high heat.
Reduce heat and simmer for about 30 minutes, skimming off any foam that rises to the surface.
Remove the chicken from the pot and set aside to cool. Once cool enough to handle, shred the chicken meat, discarding the bones and skin.
In the same pot, add the chopped onion, garlic, carrots, and celery. Cook for about 5 minutes until the vegetables start to soften.
Stir in the diced potatoes (both Yukon Gold and papa criolla if using) and corn rounds.
Add the guasca (or oregano), bay leaf, cumin, paprika, salt, and black pepper. Mix well.
Return the shredded chicken to the pot and pour in additional water if needed to cover the ingredients.
Bring the mixture to a boil, then reduce heat and simmer for another 30 minutes, or until the potatoes are tender and the soup has thickened slightly.
Remove the bay leaf from the soup.
Ladle the Ajiaco into bowls.
Garnish with a dollop of heavy cream or sour cream, a spoonful of cooked white rice, slices of avocado, capers, and a sprinkle of fresh cilantro.
Enjoy your meal!