Wash and dry all produce. Preheat oven or toaster oven to 400 degrees. Thinly slice chorizo into rounds. Cut potatoes into 1/2-inch cubes. Halve, peel, and finely dice onion. Halve and pit avocado. Scoop out flesh with a spoon, then thinly slice.

Add chorizo to a large pan over medium heat. Cook, tossing occasionally, until oil has rendered and rounds are crispy, 4-5 minutes. Remove from pan with slotted spoon and set aside, keeping as much oil in pan as possible.

Increase heat under pan to medium high. Add potatoes and cook, tossing, until crisped, 15-20 minutes. (TIP: If pan is dry, add a drizzle of oil.) Add onion and cook until softened, 3-5 minutes. Season with salt and pepper. Remove mixture from pan and set aside. Cover with foil to keep warm.

Split buns in half and place on a baking sheet cut-side up. Place a handful of cheddar cheese on each of the bun tops. Toast in oven until cheese is melted and buns are golden brown, 2-4 minutes.

Carefully wipe out pan with a paper towel, then heat a drizzle of oil in it over medium-high heat. Crack eggs into a small bowl, checking for any bits of shell. Gently slide into pan. Cook eggs sunny-side up to desired doneness, 2-4 minutes.

Layer chorizo and avocado slices inside buns, then top each with an egg to make sandwiches. Serve with hash and any remaining chorizo or avocado on the side.