Step 1

In a large bowl, mix together the chicken, mayonnaise and 3 tablespoons of lime juice until combined. Season lightly with salt. Add enough water to a large pot to come 1 inch up the sides. Set a large steamer basket inside and place the potatoes in the basket. Set the pot over medium heat, cover and bring to a boil. Steam the potatoes until fork-tender, about 20 minutes. Remove from the heat and set aside until the potatoes are cool enough to handle but are still warm. (If you like, you can peel the potatoes at this point, but that’s not necessary; see headnote.) Pass the warm potatoes through a ricer or food mill into a large bowl (do not use the coarse side of a box grater, as the texture will be too coarse). Add the aji amarillo paste, oil, 4 tablespoons of lime juice and the 2 teaspoons of salt and gently mix with your hand or spoon, until homogenous and pliable but not sticky or stiff. Line a 9-inch square baking dish that’s at least 2 inches deep with parchment paper or plastic wrap, letting the parchment overhang on all sides by about 2 inches.

Step 2

Halve and pit the avocado, then, using a large spoon, gently scoop out its flesh and thinly slice. Sprinkle the remaining 1 1/2 teaspoons of lime juice over the avocado slices to prevent discoloration.

Step 3

In a single layer, add a third of the potato mixture to the lined pan and spread evenly to cover the entire surface. Evenly spread the chicken mixture on top. Top with another third of potatoes, followed by the tomato and avocado slices, and a drizzle of mayonnaise. Finish with the remaining potatoes, cover with plastic wrap and refrigerate for at least 1 hour and up to 8 hours.

Step 4

Place a cutting board or platter on top of the pan and carefully flip over, unmolding the causa and peeling away the paper or plastic; you can also serve it straight from the dish. Garnish with the olives, eggs and parsley leaves. NOTES: To make your own aji amarillo paste from fresh or frozen chiles, discard the seeds and ribs from the chiles, place in a saucepan, cover with water, and bring to a light boil. Immediately, drain the peppers, discarding water. Repeat twice more. (This process tames aji amarillo’s heat while maintaining its flavor.) Cool the chiles slightly, then discard their skins. Transfer the chiles to a blender and process until smooth, adding a little water, if necessary.

Step 5

Dried aji amarillo can be prepared in a similar manner but will not have the same vibrant yellow hue as fresh and frozen chiles. To prepare the paste from dried chiles, place them in a pot, bring to a light boil, and immediately drain. Repeat twice, but on the last boil, leave the chiles submerged in the water until fully hydrated and plump, about 20 minutes. Once plump, drain the chiles; discard the skins, seeds and ribs; then process in a blender until smooth, adding a little water, if necessary. Freeze leftover paste in ice cube trays and transfer to a plastic bag.

Step 6

To simplify the construction, make fewer layers: Arrange half the potatoes in the dish, followed by the chicken salad and tomato-avocado-mayonnaise, and then finish with remaining potatoes. You can also layer just the potatoes and chicken salad and save the tomato and avocado for a last-minute garnish. Serve the salad from the dish.