If you're like me and have sensitive thin skin, you may want to wear gloves for this part. (Or cover your hands in vegetable oil, which they say works from preventing a reaction to the capsaicin in the chiles, but I've never found effective.)
Carefully cut off the stems off the top of the chiles and then slice open. Remove the seeds and ribs from the dried peppers (they should peel right out) and then slice the chiles into halves or thirds so they are flat.
In a dry skillet over medium-low heat, gently heat up the peppers on both sides until they just start to blister. Keep a very close eye on them, as it is easy to burn a chile into bitterness during this stage. I usually do about 20-30 seconds on each side for the ancho chiles and 10-15 seconds per side for the thinner guajillo, gentle pushing down with my tongs while they heat. This helps open up the chiles and releases their oil.
After you've heated your chiles, put them in a glass bowl or large measuring cup then cover with 2-3 cups of boiling water. Cover the bowl with plastic wrap and allow to steep for about 2 hours.
With about a half hour left on the chiles steeping time, dice the onion and saute over medium in 1 tablespoon of vegetable or canola oil until translucent. Add the garlic and heat for a few minutes more and set aside to cool slightly.
Once the chiles have had time rest, preheat the oven to 350º.
Remove the chiles from the water, reserving the liquid for later.
In a food processor or a blender, puree together the sauteed garlic and onion, the diced tomatoes, the chiles and 1 or 2 tablespoons of tomato paste depending on how concentrated of a tomato paste you are using. Then blend in 2 cups of chicken stock and ½ cup of the reserved chile soaking liquid.
Transfer to a skillet and stir in the cumin, oregano (be sure to give the oregano a good crushing between the palms of your hands, salt and pepper. Bring to a simmer and reduce heat. Allow to thicken, stirring often, for about 20-30 minutes.
While your enchilada sauce is going on the stove, roast your chicken with a touch of olive oil, salt, pepper and a light sprinkle of cumin if you wish. Cook until the juices run clear from the chicken if pricked with a fork, about 20-25 minutes. Set aside to rest until the sauce is ready.
Normally once the enchilada sauce was thickened as so, you'd run it through a strainer to remove the thicker parts of chile and tomato skins. Since we're making a dip and would like the extra heft, we're going to skip that step.
In a large shallow roasting dish (long time readers know I'm a fan of putting baked dips in shallow pans as to ensure even topping delivery, so the 9x13 pan it is!), shred the cooked chicken. Mix in the enchilada sauce and most of the shredded Monterey Jack and cheddar cheese, leaving enough to top the dip later on.
Bake at 350º for about 15-20 minutes, long enough to melt the cheese and heat up the chicken and the enchilada sauce until bubbling.
Remove the dish from the oven. Give everything a big stir and the top with the remaining cheese. Return to the oven and bake until the cheese has melted, say another 5-10 minutes.
Pipe the sour cream evenly over the top of the dip and toss on the chopped olives.
Serve with corn chips for a more manageable enchilada party experience.
Notes
Guajillo chiles are completely optional, but I think they had a nice hint of heat to the dip without being overwhelming like a chipotle or arbol. They're hotter than the anchos, without losing the rich pepper taste.
Recipe by sarah sprague at https://sarahsprague.com/2012/01/25/ancho-and-guajillo-chile-chicken-enchilada-dip-28-days-of-super-bowl-recipes/