Grilled Veal Sweetbreads Tacos (Tacos de Mollejas de Ternera a la Parilla)

Soak the sweetbreads. Slide the sweetbreads into a deep dish that will hold them in a single layer. Cover with water (or milk) and sprinkle heavily with salt. Let stand for an hour, then tip off the liquid, re-cover with water (or milk), sprinkle with more salt and let stand another hour (or covered in the refrigerator overnight). Tip off the liquid, then pat the sweetbreads dry on paper towels.

Grill the sweetbreads and onion. Light a charcoal fire and let it burn until the coals are covered with white ash and medium hot; bank the coals to one side for indirect grilling. Alternatively, heat half the burners on a gas grill to medium. Brush both sides of the sweetbreads with oil, lard or bacon drippings, then sprinkle both sides generously with salt and pepper. Lay on the hottest part of the grill and let cook until richly browned undernneath, 4 to 5 minutes, then flip them over and brown the other side. Transfer to the other side of the grill (it should be way cooler than the hot side–about 250 degrees) and let coast along for about an hour, until there is no pink left in the center (cut a piece open to check). The sweetbread lobes will feel firmer and you’ll notice that any membranes will have broken down. I like to baste the sweetbreads with a little oil, lard or bacon drippings along the way to ensure that the crusty outside stays tender.

Shortly before the sweetbreads are ready, brush both sides of the onion with oil, lard or bacon drippings and sprinkle with salt and pepper. Lay them in a single layer on the hot side of the grill and cook until richly browned on both sides, about 5 minutes total.

Serve. When the sweetbreads are ready, cut them and the grilled onion into bite-size pieces (about ½ inch). Taste and season with salt and pepper, then scoop everything into a warm bowl and set out with limes, salsa, onions and cilantro and tortillas for everyone to make tacos.