In a large pot, heat the vegetable oil over medium heat. Add the chopped onion and minced garlic, and sauté until they become fragrant and translucent.
Add the chicken pieces to the pot and cook until they are browned on all sides.
Pour in the chicken broth and bring it to a boil. Once boiling, reduce the heat to low and let it simmer for about 30 minutes, or until the chicken is cooked through and tender.
Remove the chicken from the broth and let it cool slightly. Once cooled, shred the chicken into bite-sized pieces and set it aside. Discard the bones and any skin.
Return the shredded chicken back to the pot along with the cubed Yukon gold and Russet potatoes, and the corn pieces. Add the ground cumin and some salt and pepper to taste.
Simmer the soup for another 20-25 minutes, or until the potatoes are fully cooked and tender. Adjust the seasoning if needed.
Just before serving, stir in the chopped cilantro, reserving a small amount for garnish.
Ladle the Ajiaco into serving bowls and garnish with avocado slices, capers, a dollop of sour cream or heavy cream, and a sprinkle of chopped cilantro.
Serve hot and enjoy!