In a comal or dry skillet over medium heat, toast each tortilla until pliable, about a minute per side. Feel free to wet your fingertips with water and splash the tortillas a bit as they are warming up, so they get even more flexible, especially if they are older tortillas. Set aside and keep warm.
In a skillet over low heat, bring the rustic Oaxacan sauce to a low simmer.
Heat the oil in another skillet over medium heat. When hot, using tongs, briefly fry each tortilla in the oil and then briefly dip them into the simmering tomato sauce to coat. Set aside.
Fold the tortillas in half and serve three to a plate. Top with crumbled cheese, parsley, onion, and a little more sauce and serve.
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