Combine chicken, green peas, carrot, shallot, roasted red peppers, cilantro, and lime juice in a bowl. Season with salt and cayenne. Add mayonnaise and mix until combined. Cover with plastic wrap and refrigerate until ready to use.

Place potatoes into a pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until very tender but not falling apart, about 20 minutes. Drain well and transfer potatoes to a mixing bowl. Mash until smooth.

Add ají amarillo, olive oil, and lime juice to the potatoes. Season with cayenne and salt. Mash together with a potato masher. Switch to a spatula and mix until completely smooth.

Line four 6-ounce ramekins with plastic wrap. Scoop mashed potatoes evenly into ramekins; press and smooth out the tops. Cover each with a layer of avocado slices. Fill each ramekin to the top with chicken salad, pressing it down and pulling up the plastic wrap to eliminate any air pockets. Cover with a final layer of mashed potatoes, going up to 1/2 inch or more over the rim.

Seal top with a new layer of plastic wrap and fold the sides over to seal. Refrigerate salads until completely chilled, at least 1 hour.

Mix mayonnaise, sour cream, garlic, and ají amarillo together for the sauce, adding a splash of water to adjust the thickness.