In a medium cast-iron casserole, heat 2 tablespoons of olive oil. Add the chicken and cook over high heat until nicely browned, 2 minutes per side. Add the chile powder, cumin and 1 cup of water; season with salt and bring to a simmer. Cover and cook over low heat until the chicken pulls apart easily with a fork, about 1 hour. Transfer to a cutting board or bowl and shred, then return it to the cooking liquid.
On a microwave-safe plate, microwave the tortillas at high power for 30 seconds, until soft and pliable. Transfer the chicken to the tortillas and top with the avocado and cilantro leaves. Serve immediately; pass sour cream at the table.
The pulled chicken can be refrigerated for up to 3 days; reheat gently.
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