Step 1: Rinse the beef shank and place it in a large pot. Cover with 6-8 cups of water or beef broth. Add the quartered onion and 2 cloves of garlic. Bring to a boil, then reduce heat, skim any foam, and simmer for 1.5 to 2 hours, or until the beef is tender. Season with salt to taste during the last 30 minutes of cooking.
Step 2: While the beef cooks, prepare the chiles. Remove stems and seeds from the guajillo, puya, and árbol chiles. Briefly toast them in a dry pan over medium heat for about 30 seconds per side until fragrant (be careful not to burn them). Place the toasted chiles in a bowl and cover with hot water. Let them rehydrate for 20-30 minutes.
Step 3: Roast the tomatoes. You can do this on a comal, in a dry pan, or under the broiler until softened and slightly charred. Roughly chop them.
Step 4: Once rehydrated, drain the chiles. In a blender, combine the rehydrated chiles, roasted tomatoes, 1 clove of garlic, and a small amount of the beef broth from the pot. Blend until completely smooth. Strain the mixture through a fine-mesh sieve into a separate bowl to remove any solids, pressing down with a spoon to extract all the liquid. Discard the solids.
Step 5: Once the beef is tender, remove it from the pot and shred or cut it into bite-sized pieces. Strain the beef cooking liquid into a clean pot, discarding the cooked onion and garlic. Return the beef pieces to the strained broth.
Step 6: Add the strained chile and tomato sauce to the pot with the beef and broth. Bring to a simmer. Add the corn pieces and cook for about 10-15 minutes, or until the corn is tender. Add the chopped calabacita and cook for another 5-7 minutes, or until the squash is tender-crisp.
Step 7: Add the bunch of fresh cilantro to the soup for the last few minutes of cooking, allowing its flavor to infuse. Taste and adjust seasoning with salt if needed.
Step 8: Ladle the Mole de Olla into bowls. Garnish generously with fresh chopped cilantro and chopped onion. Serve immediately with a squeeze of fresh lime juice and warm corn tortillas on the side.