Baked Eggs with Salsa Verde

Name: Baked Eggs with Salsa Verde
Ingredients: Vegetable oil, as needed; 1/3 cup Salsa Verde, recipe follows; 4 large eggs; Kosher salt and freshly ground black pepper; 1/4 cup shredded Monterey jack cheese (about 1/2 ounce); 2 tablespoons chopped fresh cilantro leaves; Corn tortillas, for serving, optional; Hot sauce, for serving, optional; Chopped scallions, for serving, optional; 1 pound tomatillos, husked and rinsed; 1 clove garlic, smashed; 1/4 medium onion; 1/4 jalapeno chile, with seeds; 1 teaspoon kosher salt; 4 sprigs fresh cilantro