First make the hatch tomatillo salsa. If you haven't roasted hatch chiles yet, place them in a 400 degree F oven and roast until skin is charred. Then remove from oven and place foil over for about 10 minutes. This will help remove the outer charred layer. Then remove seeds and reserve.
In another baking sheet, add the tomatillos, jalapeno, garlic and onion. Toss with salt, pepper and olive oil and roast at 400 degrees F for about 15-20 minutes or until the tomatillos are fork tender. Remove from oven and allow to cool for a few minutes.
Then place all roasted vegetables and hatch chiles in a food processor (or blender) with cilantro, lime juice, honey, salt and pepper. Blend until smooth or desired consistency. Taste for seasoning and set aside.
To make the red salsa, toast the dried chiles in a skillet for about 30 seconds -1 minutes turning them. They should toast slightly but not burn. Then remove chiles and place them in a bowl of warm water and allow to soak for about 30 minutes until they soften and the water turns a light red.
Then add the chiles to a food processor (or blender) with tomato, garlic, lime juice, oregano, honey and salt and pepper. Blend until smooth and add reserved soaking liquid if needed. Add a little at a time until desired consistency. Taste for seasoning and set aside.
To make the chilaquiles, Drizzle canola oil in a pan so it coats the bottom. Fry tortilla triangles in the oil until they crisp up and are slightly browned on both sides, about 1-2 minutes. Then drain well on a paper towel lined baking sheet to absorb excess oil.
In another pan, fry 2 eggs (or more if like) in butter until whites are set but yolk is still runny. When done, set aside.
To put together, place tortillas back in skillet (I used the one I fried tortillas in) and toss with a few tablespoons of tomatillo salsa. Toss gently until tortillas are covered with salsa. Then add fried eggs, red salsa, chopped hatch chiles, avocado, cojita cheese and cilantro.
Both salsa make more than needed for the chilaquiles.