In a 4-quart Dutch oven, heat oil over medium-high heat. Add onion and garlic; cook and stir for 3 minutes. Add butter, cumin, coriander, chili powder, oregano, and salt. Cook and stir until butter melts.
Add beer, tomatillos, and chile peppers. Bring to boiling. Add chicken. Return to boiling; reduce heat. Simmer, covered, about 15 minutes or until chicken is tender and no longer pink, stirring every 5 minutes to break up the tomatillos. Using a slotted spoon, transfer chicken from the cooking liquid to a cutting board. Gently boil the cooking liquid, uncovered, about 10 minutes or until thickened, stirring occasionally. Meanwhile, using two forks, pull chicken apart into shreds.
Place chicken in a medium bowl. Add 1 cup of the reduced cooking juices; stir to moisten. Use chicken mixture as filling for quesadillas or tacos; pass the remaining cooking juices.