For the green chile chicken filling: Sprinkle the chicken thighs with 1 teaspoon of the salt, and the pepper and cumin. Heat the 2 tablespoons the canola oil in a large Dutch oven over medium-high heat. Working in batches, place the chicken thighs, skin side down, in the pan and cook until browned and crispy, 5 to 6 minutes. Turn the chicken over and brown on reverse side, 3 to 4 minutes; between batches, add more canola to the pot as needed). Remove the chicken to a plate and set aside.
To the pot, add the potatoes, poblanos, onions, garlic, and the remaining 1 teaspoon salt. Saute until the onions are translucent, 5 to 6 minutes. Return the chicken thighs to the pot and deglaze with the chicken broth, stirring to scrape any browned bits. Bring to a boil, then cover and lower to a simmer. Cook until the chicken thighs are tender and the potatoes are starting to break down into the sauce, 25 to 30 minutes. Remove the chicken thighs to a plate and let cool. Remove the bones from the chicken thighs and chop meat into 3/8-inch cubes. Place the cubed chicken back in the pot, and bring back to a simmer. Continue cooking until the sauce has thickened and most of the liquid has evaporated, another 5 to 6 minutes. Remove from the heat and keep warm.
For the guajillo sauce: Remove the stems and seeds from the guajillos; tear the chiles in half lengthwise. In a large saute pan over medium-high heat, toast the chiles and garlic until they become fragrant and start to brown, about 2 to 3 minutes. Remove the chiles to a bowl and add 2 cups boiling water, or enough to just cover. Set aside to rehydrate for 15 minutes.
In a blender, add the chiles with their soaking water, and the toasted garlic, oregano, cumin and chicken broth. Puree until smooth, 2 to 3 minutes. Pour the guajillo puree into a pan and bring to a simmer; cook gently until slightly thickened, 20 to 25 minutes. Remove from the heat, and stir in the salt, sugar and pepper. Cover and keep warm.
Make the burritos: Preheat the oven to 400 degrees F.
Place the flour tortillas on a clean flat surface. In the middle of each tortilla, place about one-quarter of the chicken filling, and top with a 1/2 cup of the Chihuahua cheese. Spread the filling out slightly. Fold in the sides of the tortillas and then carefully roll them up into burritos.
In a large nonstick saute pan over medium heat, place the burritos, seam side down, and cook to lightly brown and seal, about 1 minute. Turn and cook on the reverse side. Transfer the burritos to an oven-proof platter and cover completely in guajillo sauce. Sprinkle the remaining Chihuahua cheese over the top. Bake until the burritos are golden brown around the edges and the cheese is bubbly, 7 to 8 minutes.
Garnish the burritos with a dollop of sour cream and some cilantro and scallions. Add a squeeze of lime juice and serve.
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