Prepare the Sauce Base: Heat the olive oil in a large pan over medium heat. Add the chopped onions and sauté until they become soft and translucent, about 5-7 minutes. Add the minced garlic and aji amarillo peppers chopped. Continue to cook for another 3-4 minutes, stirring frequently, until the mixture is fragrant.
Thicken the Sauce: In a small bowl, mix the cornstarch with water to create a slurry. Pour the slurry into the pan and stir continuously until the sauce starts to thicken. Add the Greek yogurt, Parmesan cheese, cottage cheese, and cashews (if using).
Blend the Sauce Ingredients: Transfer the cooked onion and ají mixture to a blender. Blend until smooth and creamy.
Return to the Pan and Add Chicken: Pour the blended sauce back into the pan. Fold in the shredded chicken breast. Season the mixture with salt and pepper to taste. Let it simmer on low heat for another 5 minutes to ensure the chicken is heated through and the flavors meld together. Taste and season with salt and pepper.
Prepare the Accompaniments: While the sauce is simmering, steam the potatoes until tender. Slice the hard-boiled eggs and black olives.
Assemble the Dish: On each plate, place a few leaves of lettuce. Add a portion of steamed potato slices. Spoon the ají de gallina sauce over the potatoes. Garnish with slices of hard-boiled eggs and black olives.