Rinse the chicken breasts and place them in a large stockpot with 10 cups of water. Add the garlic cloves, half of the chopped onion, and salt to taste. Bring to a boil over high heat, then reduce to medium-low and simmer for 40 minutes until chicken is fully cooked.

While the chicken cooks, peel the potatoes. Cut the white potatoes into large chunks. Slice the red potatoes into rounds. Cut the yellow potatoes (papas criollas) in half if large, or leave whole if small.

Remove the cooked chicken from the pot and set aside to cool. Strain the broth and return it to the pot. Once chicken is cool enough to handle, shred it into bite-sized pieces and set aside.

Add the white potato chunks to the broth and bring to a boil. Cook for 15 minutes, stirring occasionally. These potatoes will break down and thicken the soup.

Add the red potato slices, yellow potatoes, and corn pieces to the pot. Add the remaining chopped onion and cilantro. Season with additional salt and black pepper to taste. Simmer for 20 minutes until all potatoes are tender.

Return the shredded chicken to the pot and stir gently. Cook for 5 more minutes to heat the chicken through.

Taste and adjust seasoning as needed. The soup should be thick and creamy from the dissolved white potatoes.

Serve hot in deep bowls, making sure each serving has chicken, all types of potatoes, and corn. Place capers, heavy cream, and avocado slices on the table for guests to add as desired. Serve with white rice on the side.