Make the avocado salsa verde: In a food processor, combine the salsa verde, avocado, cilantro, ½ of the jalapeño, garlic clove and the juice of ½ lime. Purée the salsa until it is super creamy, stopping to scrape down the sides as necessary. Transfer the salsa verde to a small saucepan and gently warm it over medium-low heat, stirring often (or transfer the salsa to a bowl and warm it in the microwave). Don't overheat this stuff! Cover the salsa until you're ready to serve.
Cook the beans: Heat a drizzle of olive oil in a medium-sized saucepan (with a lid) over medium heat. Once the oil is warmed, add the onion and sauté for a few minutes, stirring often, until the onions are turning translucent. Add the chili powder, cumin and cayenne and stir. Add the beans and ¼ cup water and stir to combine. Cover the pan, reduce heat, and let the beans simmer for about 10 minutes (if the beans seem dry at any point, add a splash of water). Remove from heat, mash some of the beans with the back of a big spoon and cover the pan until you are ready to serve.