2 tablespoons unsalted butter (1 oz), at room temperature, plus more as needed
8 large eggs
2 radishes, trimmed and thinly sliced
1/2 cup chopped cilantro leaves and stems
1 Cup cotija cheese, crumbled or grated
Plunk the potatoes in a saucepan and add enough cold water to cover along with a teaspoon salt. Bring to a boil. Immediately drain the potatoes in a colander in the sink and rinse them under cold running water, until they are very dry and completely cool.
Heat a large, heavy-bottomed skillet over medium-high heat. Add the chorizo, spread evenly around the skillet, and cook, until nicely caramelized on the bottom, 3 to 5 minutes. Stir to get the uncooked parts of the chorizo in contact with the skillet and continue cooking until all the meat is cooked through, about 5 minutes more. Using a slotted spoon, transfer the chorizo to a large bowl.
If the skillet looks dry, add more oil to the fat in the skillet and heat over medium-high heat. Spread the potatoes evenly in the skillet and cook, stirring and turning gently with a spatula, until golden brown on all sides, about 10 minutes. Dump the potatoes into the bowl with the chorizo and mix gently. Taste and adjust the seasoning.
Pour off any excess fat in the skillet into a small heatproof bowl. Place the skillet over medium heat. One at a time, add the tortillas and fry on each side until they soften and blister slightly, about 30 seconds per side. If the skillet dries out, add a wee small amount of the reserved fat (or, if there wasn’t any fat to reserve, a little olive oil). Keep the tortillas warm by stacking them and wrapping them in a kitchen towel as they come out of the skillet.
In a small nonstick skillet, heat 1 teaspoon olive oil over medium-high heat. When the oil is hot, add a scant teaspoon butter and swirl the skillet to mix the fats. Crack an egg into the skillet and cook until the white is just set, about 3 minutes. Slide the egg carefully onto a platter you’ve rinsed with hot water and cover to keep warm. Repeat to cook the remaining eggs in the remaining butter, adding more oil as needed.
To assemble the tacos, place 2 warm tortillas on each plate and spoon a few tablespoons chorizo and potatoes in the middle of each tortilla. Top each with a fried egg and radish slices. Finish with a big pinch cilantro and a sprinkle cotija. Serve right away.