Cover the whole potatoes with cold, salted water, boil until cooked through. Remove from heat, drain and cool. Peel the potatoes and cut in half length-wise or into rounds.
Place the cheese, evaporated milk, peppers and turmeric in a blender or food processor and puree until smooth. With the motor running, add the crackers one at a time to thicken the sauce. With the motor still running, drizzle in the oil. Add more crackers if the sauce is too thin, or some milk or water if it is too thick. Season to taste with salt and pepper.
Line a serving platter with the lettuce leaves. Place the potatoes on top of the lettuce leaves. Spoon the chile-cheese sauce over the potatoes. Garnish serving plate with egg quarters and tomato wedges. Sprinkle olives over potatoes and serve cold or at room temperature.
Papa a la Huancaina is also popular in Bolivia. However, the cheese is sometimes substituted with 1 cup of natural peanut butter.
Ají amarillois the fiery yellow pepper common in Peruvian cuisine. These peppers can be found canned or in jars at many Latino markets.
Try using a variety of potatoes for a colorful effect: blue, Yukon gold, russets, etc.
A little garlic can be added to the sauce. A little lime or lemon juice squeezed in the sauce can round out its taste nicely as well.
A local herb, palillo, is often added to the sauce, imparting a further bright yellow color. It can sometimes be found in powdered form at Latino markets. Turmeric is a fine substitute.