In a medium (3- to 4-quart) saucepan, bring 1 quart of water to a boil. Dice the potatoes into ½-inch cubes, and heavily salt the water (you'’ll need about 2 teaspoons). Simmer over medium heat until the potatoes are fully tender, about 10 minutes. Drain.
(Note: Chef Bayless uses a quarter of a large onion, but this recipe calls for half of a small onion.) Finely dice onion and place in a large skillet over medium-high heat, and immediately add the chorizo. Cook, breaking up any lumps of chorizo, until the onion is soft and the sausage cooked through, about 10 minutes. If the chorizo has rendered more than a light coating of fat over the bottom of the skillet, pour out the extra.
As the chorizo cooks, make the avocado salsa: Roughly chop the husked, rinsed tomatillos; chop the garlic clove; chop the chiles. In a food processor, combine the tomatillos, garlic, and chiles, and pulse until finely chopped (scraping down the sides of the processor as necessary). Add the peeled and pitted avocado, season with ½ teaspoon salt, and pulse until everything is well blended; the sauce should be the consistency of a light mayonnaise. Salt to taste, then scrape the sauce into a serving bowl and set aside.
Use a slotted spoon or strainer to drain the potatoes thoroughly; add them to the skillet with the chorizo mixture and continue to cook over medium heat, stirring regularly until the potatoes begin to brown, 7–8 minutes. As the mixture cooks, coarsely mash everything together with the back of a spoon or a spatula, scraping up any crusty bits of potato, so that it roughly holds together (it will look a little like hash). Cover and keep warm over the lowest heat.
Serve the potato-chorizo mixture with the avocado sauce and warm tortillas. (To reconstitute or reheat store-bought tortillas, wrap the stack in a damp paper towel and heat in the microwave on full power for 1 minute.)