Heat a gas grill to medium-high on one side, medium on the other, or light a charcoal fire and let it burn until the charcoal is covered with white ash, then bank the coals to one side. Using an oil mister or pastry brush, oil each onion round on both sides and lay on the hottest side of the grill. Cook, flipping them half way through, until soft and grill-marked, 8 to 10 minutes. Let cool, then cut into ½-inch pieces.
Place shrimp on skewers for easy cooking. Oil the shrimp on both sides and lay the hottest side of the grill. Cook, flipping halfway through, until just cooked through, about 5 minutes total. When the shrimp is cool enough to handle, cut them in half through the back making two crescents.
Lay the tortillas on the cooler side of the grill. Top each with about ¾ cup of cheese and cook until the cheese starts to melt. Divide the grilled onion and shrimp among the tortillas. When the cheese is about half melted, fold the tortillas in half, enclosing the filling. Cook the quesadillas until the tortillas are lightly grilled and the filling is warmed through, about 2 minutes per side. Serve without hesitation, with Salsa Huevona for guests to use to their taste.
Ok, I know the name’s a little edgy, since many people wouldn’t use huevona around their grandmother. Perhaps I should have translated salsa huevona as ‘lazy-ass salsa,’ more clearly capturing to the sentiment one of our cooks was expressing when he christened this salsa. That was after his cousin put tomatoes, onions and jalapeños on the backyard grill one Sunday afternoon and promptly forgot them until they were nearly throw-away blackened. And then he decided to use them anyway, which actually was to his credit, because something, well, alchemical seemed to happen. Alchemical and quite delicious. Though rustic and a little huevona.
This salsa keeps well for 3 or 4 days in the refrigerator, covered.
Makes 2 ½ cups, serving 6 generously
1 ½ pounds (4 medium-small round) ripe tomatoes
1 medium white onion, cut in half
3 or 4 fresh jalapeños, stemmed
4 unpeeled garlic cloves
Heat a gas grill to medium-high or light a charcoal fire and let it burn until the charcoal is covered with white ash. Lay the tomatoes, onion halves, jalapeños and garlic on the hot grill. (To keep the garlic from dropping through the grates and to make cleanup easy, I typically lay one of those perforated grill pans on the grill grates, heat it up, then lay on the vegetables.) Grill the ingredients, turning occasionally, until they are kind of charred, but not incinerated—about 10 minutes for the garlic, 15 minutes for the chiles and 20 minutes for the tomatoes and onions. As they are done remove the ingredients to a rimmed baking sheet. Let cool. Peel the garlic. If you wish, you can pull the charred skins off the tomatoes.
In a food processor, combine the garlic and chiles. Pulse until coarsely pureed. Add the tomatoes and any juices that have collected on the baking sheet, and pulse until roughly chopped. Chop the charred onion and place in a bowl. Stir in the tomato mixture, along with a little water (usually about 2 tablespoons), to give the salsa an easily spoonable consistency. Taste and season with salt, usually about 1 teaspoon.