Preheat the broiler. Mix 1 tablespoon olive oil with the grated garlic, oregano and paprika in a small bowl. Rub all over the pork chops on a rimmed baking sheet; season with salt and pepper.
Toss the hominy, green beans, pimientos and smashed garlic with the remaining 1 tablespoon olive oil, 1/2 teaspoon salt and a few grinds of pepper in a large bowl. Scatter around the pork chops. Pour the chicken broth over the hominy mixture, then dot with the butter.
Transfer the baking sheet to the broiler and cook, rotating the pan and stirring the hominy mixture halfway through, until a thermometer inserted into the pork registers 145˚ F, 9 to 12 minutes. Remove the pork chops to plates.
Stir the hominy mixture and return to the broiler until some of the liquid is reduced and the green beans are charred, 1 to 2 more minutes. Stir in the vinegar, season with salt and add to the plates.