Preheat the oven to 500 degrees F. In a saucepan combine the red onion, vinegar, pickling spices and salt and bring to a simmer. Cook for 3 to 4 minutes, stirring occasionally. Transfer mixture to a bowl and chill. In a heavy skillet heat 2 tablespoons of the olive oil over moderately high heat and cook the onion until tender and golden. Add the cumin, salt and pepper and cook until the aroma of the cumin is released, about 1 minute. Add the beans and water and cook, stirring and mashing until beans are coarsely mashed, about 5 minutes. Taste and adjust seasoning with salt and pepper if necessary. Brush one side of 2 tortillas with remaining oil and place, oil-side down, on a baking sheet. Divide the bean mixture between the 2 tortillas and sprinkle each with a 1/3 cup of the cheese. Cover with the remaining 2 tortillas and lightly brush with oil. Bake the quesadillas in the middle of the oven until golden, about 8 to 10 minutes. Sprinkle the remaining cheese over each quesadilla and continue to bake until the cheese melts. Transfer the quesadillas to a cutting board and cut into 6 wedges. Top each wedge with a small dollop of sour cream, some pickled onion and a sprig of cilantro. Serve immediately.
Adapted from a recipe by Gourmet Magazine