In a 9-by-13-inch glass or ceramic baking dish, stir together 2 tablespoons oil, the beer, garlic, soy sauce, vinegar, ají panca, oregano, cumin, 1 teaspoon salt and 2 teaspoons pepper.
Add the chicken and turn to coat. Cover and refrigerate for at least 1 hour or up to 24 hours, turning the chicken once about halfway through marinating.
Heat the oven to 450°F with a rack in the lowest position. Remove the chicken from the marinade; discard the marinade. Pat the chicken dry and season lightly with salt.
In a 12-inch oven-safe skillet over medium-high, heat the remaining 1 tablespoon oil until shimmering. Add the potatoes in an even layer and cook, uncovered and without stirring, until lightly browned at the edges, 2 to 3 minutes.
Place the chicken skin side up on top of the potatoes. Transfer the skillet to the oven and roast until the chicken is deeply browned and the thickest part of the leg quarters reach 175°F, about 45 minutes.
Remove the pan from the oven (the handle will be hot). Let rest for about 10 minutes, then transfer the chicken and potatoes to a serving platter. Sprinkle with the cilantro and serve with ají verde (if using).
