Toss the avocado, about one-quarter of the onion, 2-1/2 tablespoons of the lime juice, and 2 tablespoons of the cilantro in a medium bowl. Season with salt and pepper to taste and set aside.

In a food processor, combine 1 cup of the beans, the tomatoes and their juice, the chipotles, and adobo sauce and process until smooth. Set aside.

Season the chicken with 1 teaspoon salt and 1/2 teaspoon pepper. Heat the oil in a large Dutch oven or casserole over medium-high heat until it's shimmering hot. Add the chicken (the thighs should just fit, evenly spaced) and sear without touching until golden brown, 3 to 4 minutes. Flip and cook the other side until also golden brown, 3 to 4 minutes. Transfer to a large plate and let rest for 10 minutes.

Take the pot off the heat and set aside. When the chicken has rested, shred it by hand or chop it coarsely.

Return the pot to medium-high heat. Add the remaining onion to the pot and cook, stirring, until the onion begins to brown and soften, about 3 minutes. Add the chili powder and cumin and stir for 20 seconds. Add the beer and cook, scraping the bottom of the pan with a wooden spoon to incorporate any browned bits, until it almost completely reduces, 3 to 4 minutes. Add the remaining white beans and the pureed bean mixture and bring to a boil. Stir in the chicken along with any accumulated juices on the bottom of the plate. Cover, reduce the heat to medium-low and simmer for 15 minutes so the chicken finishes cooking and the flavors mix and meld. Stir in 1-1/4 cup of the cilantro and the remaining lime juice and season with salt and pepper to taste.

Ladle into large bowls and serve immediately with a generous spoonful of the avocado mixture, a dollop of sour cream (if using), and a sprinkling of the remaining cilantro.

Serving Suggestions: Serve with Mexican rice or cornbread.