Step 1: Season the meats. Season the chicken, pork, and beef with garlic, oregano, sour orange juice, salt, and pepper. Let it sit at least 15 minutes, or overnight in the fridge if you have time. The longer, the better.
Step 2: Brown the meats. In a large heavy pot, heat the avocado oil over medium-high heat. Brown the meats in batches. Don't crowd the pot. You want color on the outside, not steam. This step builds the flavor base of the whole stew.
Step 3: Make Mami's auyama cream. While the meats are browning, place 1 cup of auyama, the onion, green pepper (ají), 2 garlic cloves, half the oregano, the cilantro, and the culantro in a separate pot. Cover with about 2 cups of water or bone broth and boil for 15 to 20 minutes, until the auyama is completely tender. Blend until smooth and golden. This cream is the base of the whole sancocho.
Step 4: Add the cream, broth, and meats. Return all the browned meats to the big pot and pour Mami's cream over them. Add the bone broth and enough water to cover everything by about 2 inches. Bring to a boil.
Step 5: Add the víveres. Once it boils, add the yuca, plantain, and the remaining cup of auyama. Reduce to a steady simmer. That second round of auyama will slowly melt into the broth, so with the cream underneath, you get the thick, golden caldo without any extra work.
Step 6: Simmer low and slow. Cook uncovered on low to medium heat for 60 to 75 minutes, stirring occasionally. Skim off any fat that rises to the top. The broth is ready when it coats the back of a spoon and the meats fall apart easily.
Step 7: Taste and finish. Adjust the salt. Add a squeeze of fresh lime or sour orange directly into the pot right before serving. This wakes up every flavor in the broth.
Step 8: Serve. Ladle into deep bowls, meat and broth first. Serve with a measured portion of white rice on the side, ripe avocado, and an extra squeeze of lime.
Recipe card notes: For a thicker broth, let the auyama cook until it fully dissolves into the caldo. It does all the work on its own. If you prefer more broth, add ½ cup of water at a time during the last 20 minutes.