Heat the olive oil in the pressure cooker over medium heat. If using the Instant Pot, press the Sauté button. Add the onion and garlic and cook until the onions are soft and translucent.
Break the top stem from the chiles and discard. Shake away any seeds that fall easily out of the chiles, but don’t fuss getting them all out. Rinse the whole chiles and add them to the onions and garlic. Stir in the tomatoes, butternut squash, vegetable broth, hominy, beans and oregano. Close the lid.
Using the Instant Pot, set the top valve to Sealing. Press Cancel and then press Manual. Adjust the time for 5 minutes. Using the stovetop pressure cooker, bring to pressure and cook 5 minutes.
With the Instant Pot, let the pressure release naturally for 10 minutes, then turn the top valve to Venting to release the rest of the pressure. For stovetop pressure cookers, remove from heat and let the pressure release naturally for 10 minutes, then run cold water over the lid to release any remaining pressure.
While the pozole simmers prepare the add-ins, including lime wedges. Arrange everything in separate bowls, so, at the table everyone can add the condiments to suit their own taste.
Carefully remove the chiles from the soup. Discard the chiles. Adjust the seasoning to your taste with salt and red pepper flakes.
Ladle the pozole into large bowls. At the table, let everyone squeeze a lime wedge or two into their bowl and garnish as they wish, with cilantro, pumpkin seeds, radishes, and avocado. If desired, offer crumbled cheese and/or tortilla chips.