If using whole ají amarillo chiles, thaw them if necessary. And begin by slicing them in half. Remove the stem and seeds.
In a small sauté pan, set over medium heat, add a teaspoon of oil, reserving the rest of the olive oil. Cook the ají amarillo chiles until softened. Transfer to a blender. If you're using paste, you can simply add the paste to a blender and proceed as instructed below.
To the same small sauté pan, add the onion, garlic, and pinch of salt. Cook until mostly softened, about 3 to 4 minutes. Transfer to the blender, along with the cubed queso blanco, evaporated milk, and ground turmeric (if using); blend until mostly smooth.
With the blender running, slowly add about a tablespoon of olive oil. Add about 3 to 4 crushed saltine crackers and blend again until it reaches a thick rich consistency. Add another cracker if the consistency seems too thin. Salt to taste.
Slice the peeled potatoes into ¼-inch slices. To plate the dish, arrange the leaves of lettuce on a large plate. Fan the sliced potatoes atop the lettuce, and pour the sauce over the potatoes. Garnish with eggs and olives.
