Peel yucca and cut into 4 cylinders; then split in half and remove the root. Place yucca in a large pot. Add enough water to cover yucca and season with salt. Bring to a boil and simmer until fork tender, about 30 minutes.
Remove from heat and allow to cool. Brush with butter and place on grill. Cook about 3 to 4 minutes per side. Remove and season with salt.
Meanwhile, in a skillet, heat 2 tablespoons oil over medium heat. Add onion, aji, and garlic. Season with salt and pepper and saute until onion becomes translucent. Remove from heat and add to blender. Add cheese and hard-boiled egg and blend. Slowly drizzle in heavy cream and remaining 2 tablespoons oil until sauce consistency. Adjust salt before serving.
Serve yucca with huancaina sauce, garnished with hard-boiled egg, olives, and cilantro.