Scoop the potato into a microwave-safe bowl, cover with plastic wrap, poke a few holes in the top and microwave on high for 3 minutes.
Lay the chorizo and onion in a very large (12-inch) skillet (preferably non-stick) and set over medium heat. Cook, stirring frequently and breaking up clumps, until the fat renders, the sausage looks cooked, and the onions are translucent, about 6 minutes.
Scoop the potatoes, leaving the steaming liquid behind, into the skillet and continue cooking until the potatoes are soft, about 5 minutes. If the potatoes begin browning long before they’re soft, reduce the temperature a little. Taste and season with salt if you think the mixture needs it—some chorizo is so highly seasoned, little additional salt will be needed.
To serve, scoop the mixture into a deep bowl. Set out with the cheese, cilantro salsa, avocado and warm tortillas.