1. Heat broiler, with rack in top position. Place poblano on a rimmed baking sheet and broil until charred, 7 to 10 minutes, flipping halfway through. (Alternatively, roast over a low gas flame.) Transfer to a bowl, cover tightly with plastic wrap, and let steam 10 minutes. Rub with a paper towel to remove skin. Discard stem and seeds and slice poblano into 2-inch strips.

2. Meanwhile, in a large nonstick skillet with a lid, bring potato to a boil in 1 cup cold water. Cover, reduce heat, and simmer until tender when pierced with a knife, about 7 minutes. Drain potato and return to skillet. Add chorizo and cook over medium-high, breaking up meat with a wooden spoon and stirring occasionally, until sausage is cooked through and potato begins to brown, about 5 minutes. Add eggs and cook, stirring, until cooked through, about 2 minutes. Serve with tortillas, poblano strips, and salsa.