Preheat oven to 375° and line two baking sheets with parchment paper. In a medium skillet over medium heat, heat oil. Add onion and cook until slightly soft, 3 minutes. Add garlic and spices and cook until fragrant, 1 to 2 minutes more. Add chicken and enchilada sauce, then bring mixture to a simmer. Stir in cilantro, season with salt, and remove from heat.
Make taquito shells: In a medium bowl, mix together cheeses. Divide mixture into twelve 3 ½" piles on prepared baking sheet. Bake until cheese is melty and slightly golden around the edges, about 10 minutes. Let cool 2 to 4 minutes, then peel shells off parchment. Add a small pile of chicken to each and roll tightly. Repeat until all taquitos are made.
Garnish with cilantro and serve with sour cream, for dipping.
