For the red chile sauce: Soak corn husks in hot water until pliable, about 2 hours.
Meanwhile, boil garlic, guajillos, pasillas and onion in water until the vegetables soften, about 10 minutes. Blend the vegetables in a blender with 1 cup of the cooking liquid until smooth (see Cook's Note). Strain the mixture, discarding the seeds and pulp.
Heat the canola oil in a saucepan over low heat, then add the flour and cook, whisking, until a roux has formed, a few minutes. Add the chile mixture, then season with salt, pepper and cumin. Cook for an additional 15 minutes. Set aside.
For the achiote chicken thighs: Preheat the oven to 375 degrees F.
Mix achiote paste with 3 ounces olive oil by hand until a soft paste forms. Rub chicken thighs with the paste and place in a roasting pan. Bake until cooked through, 30 to 45 minutes.
Chop the chicken into 1/4-inch cubes and mix well with 1 cup red chile sauce.
For the tamales: Mix masa, baking powder, chicken stock and 1 1/2 cups extra virgin olive oil by hand until it is spreadable but still holds its shape.
Spoon about 2 tablespoons masa into the center of the wider portion of the husks, then place 2 tablespoons achiote chicken in the center along with a piece of jack cheese.
Roll up the husk, keeping the top open, and folding the narrower side over to seal the bottom.
Place the tamales, open-end up, in a steamer basket and steam over a pot of boiling water, covered, for 1 hour.
Let the tamales rest for 1 hour, then serve with additional red chile sauce.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.