Prep: Peel and cube the squash and potatoes, dice the onion and mince the garlic. Calabaza can be tricky to peel; a little skin left on is fine.
Make the base: Warm the oil in a large pot over medium-low heat. Cook the onion for 6-7 minutes, stirring, until soft and translucent. Add the garlic and cook 1 minute. Stir in the ají amarillo, huacatay and oregano and cook 2 minutes, until fragrant and slightly darker.
Simmer the vegetables: Add the squash, potatoes, 2 cups broth, salt and pepper. Bring to a boil, then cover and simmer on low for 25-30 minutes, until the squash is falling apart and the potatoes are very tender.
Mash: Use a potato masher to mash about half the pot right in the pan. Leave some chunks. It should be thick and creamy, like a stew. If it's too stiff, add broth ¼ cup at a time.
Add corn and peas: Stir in the choclo and peas and simmer uncovered for 8-10 minutes, stirring now and then so the bottom doesn't stick. Taste and adjust salt.
Serve: Spoon over or beside white rice and top with cilantro.