In heavy skillet heat 2 tablespoons oil over moderately high heat until hot but not smoking and saute chopped onion with salt to taste until softened and golden. Add cumin and cook, stirring, 1 minute. Add beans and water and cook, stirring and mashing, until beans and coarsely mashed, about 5 minutes. Season bean mixture with salt and pepper.
Put 2 tortillas on a baking sheet and brush with some remaining oil. Turn tortillas over and top each with half of bean mixture and 1/3 cup Monterey Jack, spreading evenly. Cover with remaining 2 tortillas and brush tops of quesadillas with remaining oil.
In a large saute pan, over medium heat, cook quesadillas until golden brown on each side. When complete top the quesadillas with the remaining bit of cheese. Transfer quesadillas to a cutting board and cut into wedges.
Top wedges with pickled onion and coriander sprigs.
In a small saucepan simmer ingredients for 2 minutes and transfer to a bowl. Chill onion, covered.
Per serving: 1695 Calories (kcal); 76g Total Fat; (39% calories from fat); 38g Protein; 219g Carbohydrate; 0mg Cholesterol; 3452mg Sodium Food Exchanges: 13 Grain(Starch); 1/2 Lean Meat; 3 Vegetable; 0 Fruit; 15 Fat; 1/2 Other Carbohydrates