If desired, roughly chop the onion and red pepper and pulse them with the garlic in a food processor until coarsely chopped; otherwise finely dice by hand.
Heat the olive oil in a large cast-iron pan over medium-high heat (or use the sauté function on the pressure cooker). Add the diced onion, red pepper, and minced garlic and cook, stirring occasionally, until softened, about 7–9 minutes.
Add the paprika, garlic powder, ground cumin, and dried oregano to the pan and sauté for about 1 minute until fragrant, then scrape the mixture into the Instant Pot or slow cooker using a spatula.
Rinse the dried black beans in a fine-mesh strainer and pick through them to remove any shriveled beans or debris.
Add the rinsed beans, water, and chicken or vegetable stock to the cooker. Stir in the chipotle peppers in adobo and the bay leaf, then season with salt and pepper (about 2 teaspoons salt and 1/2 teaspoon pepper to start, adjust later).
Slow cooker method: Cover and cook on high for 7–9 hours, or until the beans are very tender.
Pressure cooker method: Seal the Instant Pot, set to manual/high pressure for 45 minutes (it will take ~15–20 minutes to come to pressure). Allow a natural pressure release for 25 minutes, then release any remaining pressure manually.
Open the cooker, taste, and adjust seasoning, adding salt slowly until the flavors are balanced. Remove and discard the bay leaf and remove the chipotle peppers if you prefer less heat.
Stir in chopped cilantro and a squeeze of fresh lime juice if using. Serve warm as a side or use in other recipes; beans will thicken and develop more flavor as they rest.
