Heat the oven to 300°F.

In a microwave-safe bowl, toss together the cubed potato, a pinch of salt, and 2 teaspoons of the olive oil.

Cover the bowl with plastic wrap and microwave for 4 minutes, stirring halfway through.

Check to see if the potatoes are tender. If not, continue to microwave in 30-second bursts until done.

Warm 2 teaspoons of the olive oil in a large nonstick frying pan over medium-high heat.

Add the potatoes and cook until browned, about 5 minutes.

Transfer to a medium bowl and set aside.

Crumble the chorizo into the same pan and cook, stirring and breaking up the meat, until cooked through, about 5 minutes.

Add the chorizo to the bowl with the potatoes and cover to keep warm. Wipe out the frying pan.

Put the tortillas in the oven to warm while you cook the eggs (the tortillas should end up warm but still pliable).

Whisk the eggs in a medium bowl until broken up.

Season with a pinch each of salt and pepper and beat to incorporate.

Add the remaining 2 teaspoons of olive oil to the wiped-out pan and set it over medium-low heat.

Pour in the eggs and let them sit undisturbed until they begin to set around the edges, 1 to 2 minutes.

Using a rubber spatula, push the eggs from the edges into the center and let sit again for about 30 seconds, then repeat every 30 seconds until they’re softly scrambled. The total cooking time should be about 5 minutes.

Divide the eggs between the warm tortillas. Top with the chorizo, potatoes, cheese, cilantro, and salsa.

Fold the short sides in and the bottom flaps up, then roll into burritos and serve!