Preheat oven to 450 degrees F.
Place a rimmed baking sheet into your oven while it's preheating and keep it there until it is needed. This is to purposefully get the baking sheet hot.
Add diced potatoes to a large stock pot and fill with water, 1" above potatoes, and add 1 tablespoon of salt.
Bring to a boil and let boil 5 minutes.
After 5 minutes, drain potatoes and transfer to a large bowl.
Pour melted butter over the potatoes and stir well to combine. It is okay to break up the potatoes a little bit.
Remove hot pan from the oven (with an oven mitt!) and spread potatoes out on pan. Sprinkle with remaining 1 teaspoon of salt.
Roast in oven for 20 minutes, then stir and roast another 15 minutes, until they are golden and crispy.
Meanwhile, in large saucepan or cast-iron skillet, cook chorizo, about 8-10 minutes, breaking it up as you go.
Add onion and green chiles and cook another 5-7 minutes, until soft.
Once the potatoes are done cooking, remove from oven and lower oven temperature to 375 degrees F.
Spray 9x13" casserole dish with cooking spray, or you can use the cast-iron skillet you used to cook the chorizo if it's big enough to fit the potatoes.
Combine potatoes with chorizo mixture and pour into prepared casserole dish or skillet.
Make 6 indentations in the mixture for the eggs, then break each egg over each one.
Bake in preheated oven for approximately 12-14 minutes, until eggs are cooked but yolk is still runny.
Serve immediately and enjoy!