Causa Limena (Peruvian Potato Salad)

Mash potatoes with chili powder or cayenne pepper, turmeric, salt, and oil. You may also add the juice of a lime, but don't make the potatoes too wet. They should be stiff, relatively smooth, and very well seasoned. Allow to cool to room temperature, if not already cold.
Oil a loaf pan or other deep-walled dish (I use a casserole). Press half of potato mixture into loaf pan, creating a flat surface. Arrange vegetables and mayonnaise, or "chicken" salad (I like to keep the avocadoes in this case), atop potatoes in a more-or-less even set of layers, and then top with the remaining potatoes, smoothing the top flat. The effect should be something like a layer cake. Chill. You may decorate the top (or turn out the whole shebang onto a platter when cold and decorate the bottom!) with piped on mayonnaise, ketchup, arranged peppers and olives, or what have you.
I do not like ketchup on this, but Peruvian cooks often use it for contrast; they almost always use copious amounts of mayonnaise to decorate, either piped on in a lattice or spread on (too much!!)
This will be very firm when cold: do chill it, but don't let it sit in the fridge for ages-- it's best on the day it's made. Serve in slices. It will be very rich and is an unusual appetizer--very tasty and also festive to the eye, if your guests can stand the idea of cold potatoes!
This dish is made in Peru with a few different fillings: either a salad of chicken, chopped celery, and mayonnaise (with infinite variations), a mayonnaisey tuna salad, or vegetables, as above. Sometimes peas are included in any variation. Do include the avocado-- it's really special.
A squeeze of lime juice on the veggies makes it tastier and keeps the avocado from going brown, although with a good layer of taters on top it's anaerobic and doesn't usually brown.