Preheat oven to 375°F and grease a 9x13-inch casserole dish, set aside.
Set a large skillet over medium-high heat with 1 tablespoon oil. Once hot, add the chorizo and begin breaking it up with a wooden spoon. Cook until the chorizo has cooked through and begun to brown, about 5 to 8 minutes. Transfer to a plate and set aside.
Peel the potatoes and grate using the large holes of a box grater. Transfer to shredded potatoes to a large bowl filled with cold water. This will remove excess starch and prevent the potatoes from turning brown. Drain and then transfer the potato shreds to a clean kitchen towel. Pat dry very well.
Using the same skillet you cooked the chorizo in, set over moderate heat. Add the remaining oil and once hot, add the shredded potatoes. Season liberally with salt and pepper and stir to combine. Then using a spatula press the potatoes together to pack them in. Cook for about 2 to 3 minutes to fully brown the bottom. Flip over the potatoes to cook the second side. Once done, remove from the heat and set aside to cool slightly.
In a large bowl, whisk together the eggs, milk and a pinch of salt and pepper until evenly combined.
To assemble the casserole, place two tortillas on the bottom of the prepared casserole dish, overlapping to make them fit. Top with the browned chorizo, spreading out to create an even layer. Top with the browned hash browns and then pour in the beaten egg mixture. Bake until puffed up and almost done, about 20 to 25 minutes. Remove from the oven and then top with half of the shredded cheese. Place the remaining two tortillas on top and then finish off with the remaining cheese. Return to the oven and cook for another 10 minutes, to finish cooking the center of the casserole and melt the cheese.
Meanwhile, to make the salsa, cut the stems off the dried chiles and remove the seeds. Place a saucepan over moderate heat with the oil. Once hot, add the arbol chiles and cook for about 1 to 2 minutes to toast. Add the hot water, turn off the heat and then cover with a lid. Allow to sit for about 15 minutes or until the chiles have softened and cooled somewhat. Place all the remaining ingredients into a blender, along with the drained arbol chiles. Blend on high until the salsa is smooth. Season with salt and pepper to taste. Cover and refrigerate until ready to use.
Cut the casserole into squares and serve with the salsa, avocado or sour cream! Enjoy!