Heat oil in a Dutch oven or large pot over medium-high heat until shimmering. Add chicken thighs and cook until well browned, about 6 minutes. Flip thighs and continue to cook until other side is lightly browned, about 3 minutes. Transfer chicken to a plate, leaving fat in pan, and set aside.
Add onions and garlic to the same Dutch oven and cook, stirring occasionally, until onions have browned around the edges, about 5 minutes. Add tomatillo and cook until browned around the edges, about 4 minutes. Add oregano and cumin and cook until fragrant, about 30 seconds. Add tomatoes, chipotle, and adobo sauce and stir to combine. Remove from heat.
Transfer sauce to a blender and puree until smooth. Pour sauce back into pan, stir in chicken stock and bay leaf, and bring to a boil over medium heat. Nestle chicken thighs in sauce, reduce to a simmer, and cook until chicken is fully cooked and easily shredded, about 20-30 minutes. Transfer chicken to a plate and let sit until cool enough to handle. Remove sauce from heat and discard bay leaf.
Pull chicken meat into strips. Stir chicken into sauce and cook over medium heat until warmed through, about 3 minutes. Remove from heat and season with salt to taste.
To assemble, place a fried tortilla on a plate and top it with a smear of warmed refried beans, about a 1/2 cup of Chicken tinga, some finely shredded cabbage, a few tablespoons of freshly shredded Monterey jack cheese, as many avocado slices as you want, a heathy spoonful of pico de gallo, some sliced scallions, fresh cilantro, thinly sliced jalapeños and serve it alongside some additional lime wedges