Make this when it’s Sunday and you’re not leaving the house. One spoonful of this smoky-spicy guajillo braising liquid and you’ll understand how complex dried chiles can be. When soaked in hot water and blended with aromatics, they create a base so flavorful you don’t even need stock. The chile purée may seem like a lot of liquid at first, but don't worry: Keeping the pot slightly uncovered as the ribs cook will allow the sauce to reduce and concentrate.
Step 1
Season ribs with salt. Let sit at room temperature 1 hour, or chill, uncovered, up to 12 hours. If chilling, let sit at room temperature 1 hour before cooking.
Step 2
Meanwhile, place chilies and 5 cups hot water in a blender and let sit while you prep onion and garlic.
Step 3
Heat broiler. Broil onion and garlic on a rimmed baking sheet, undisturbed, until charred on top (don’t worry if they get super dark), 8–10 minutes.
Step 4
Pop garlic out of their skins and place garlic, onion, red pepper flakes, coriander, cumin, and cinnamon in blender with chilies. Blend until smooth but still speckled with chiles; season purée lightly with salt. Set aside.
Step 5
Heat 2 Tbsp. oil in a medium heavy pot over medium-high. Working in 2 batches, cook ribs, turning occasionally and reducing heat if needed, until browned all over, 10–12 minutes per batch. Transfer to a plate.
Step 6
Carefully pour off oil and wipe out pot. Pour remaining 1 Tbsp. oil into pot and place back over medium-high heat. Add tomato paste and cook, stirring often, until tomato paste begins to separate and stick to pot, about 3 minutes. Stir in chili purée. Return ribs to pot and bring liquid to a simmer. Partially cover pot and cook, reducing heat to low to maintain a very gentle simmer, turning ribs occasionally, and skimming any excess fat from surface, until meat is very tender, 3–3½ hours. (Make sure there's a gap between lid and pot so liquid can reduce.)
Step 7
Add squash to pot and push down so it’s mostly submerged. Bring to a simmer and cook, uncovered, until squash is tender and liquid is thickened, 18–20 minutes. If squash and meat become tender but liquid isn't thickened, transfer squash and meat to a plate and continue to cook until liquid has reached the desired saucy consistency.
Step 8
Serve ribs and squash, topped with yogurt and cilantro, with lime wedges.
Step 9
Do Ahead: Ribs (without toppings) can be made 3 days ahead. Cover and chill.