Roasted Duck With Picadillo Stuffing

3 cups kosher salt
1 cup packed brown sugar
4 inches canela sticks, or substitute 2 inches regular cinnamon sticks
12 whole allspice
6 bay leaves
40 peppercorns
4 five-pound ducks
kosher salt and pepper to taste
cilantro or flat-leaf parsley, for garnish

Prepare brine: Four hours to a day ahead, put first 6 ingredients and 2 gallons water in a stockpot and boil just until salt and sugar are dissolved. Cool to room temperature, then chill for at least 2 hours.

Prepare birds: Trim off and discard large, visible pieces of fat. Put ducks in brine, adding water to cover if necessary. Cover and refrigerate 4 to 8 hours. Remove, rinse, and pat dry.

Cook birds: Preheat oven to 400 degrees. Sprinkle birds inside and out with salt and pepper and prick skin in several places. Roast on rack, breast side up, for 15 minutes. Lower temperature to 350 degrees and roast until a cooking thermometer stuck in the thickest part of thigh or breast reads 165 degrees, for medium, or 170, for medium to well-done. Let rest 10 minutes before carving.

To serve, mound picadillo in center of plates. Carve ducks, slice breast meat, and arrange pieces on top. Garnish with sprigs of cilantro or parsley. Serves 6.

PICADILLO

3 tablespoons olive oil
1 cup finely diced onion
2 tablespoons minced garlic
1/2 cup seeded, deveined, and minced jalapeños
1 1/2 pounds (about 8 cups) mild-flavored exotic mushrooms, cleaned with damp paper towels and sliced 1/4 inch thick (if cost is a consideration, substitute white button mushrooms; get presliced if possible)
1/4 cup sherry vinegar
1 cup currants or diced cranberries (or less to taste)
1/2 cup shelled pistachios
1/8 to 1/2 teaspoon ground canela (or more to taste), also called Mexican cinnamon, an aromatic papery bark, available at Fiesta market; grind in a coffee grinder, or substitute 1/8 to 1/4 teaspoon regular cinnamon (optional)
1/8 to 1/2 teaspoon toasted ground cumin, or more to taste (optional)
kosher salt to taste

In a large sauté pan over medium heat, add olive oil and sauté onion for about 2 minutes; do not brown. Add garlic and jalapeños and sauté for about 30 seconds, being careful not to burn garlic. Add mushrooms and sprinkle very lightly with salt, tasting as you go, until flavor is right. Cook, stirring occasionally, until mushrooms release all their moisture, 15 to 20 minutes. As mushrooms begin to stick, deglaze pan with sherry vinegar. Add currants and pistachios and cook until currants are rehydrated. Add canela and cumin a little at a time, tasting, as they are quite distinctive