For the chicken: Bring the salt, sugar and 10 cups water to a boil in a pot. Remove the brine from the heat and let cool.
Cut the chickens in half and carve out the carcass, being sure to leave the thigh and leg attached to the breast. Submerge the chicken halves in the brine and let sit for 20 minutes. Remove the chickens from the brine and pat dry.
While the chickens are brining, toast the coriander seeds, fennel seeds and red pepper flakes in a hot, dry skillet. Let cool, then grind in a spice grinder and mix with the olive oil. Cut the orange into thin slices and set aside.
Transfer the chicken halves to a large baking dish and thoroughly coat with the spice oil. Cover the chickens with the orange slices and let sit.
Meanwhile, for the tomato vinaigrette: In a blender, puree the tomatoes until smooth. With the blender on low, add the vinegar, and then slowly drizzle in the olive oil. Season with salt. Pass through a tamis or fine-mesh sieve, discarding the pulp.
Prepare a charcoal grill for indirect-heat cooking (use wood charcoal if possible).
Season the chicken with sea salt and place on the grill, skin-side down. Top each chicken half with a foil-covered brick. Cook the chicken about three-quarters of the way through on the skin side, then flip and finish cooking until the juices run clear, about 20 minutes total.
Meanwhile, cut the bread into 1/2-inch-thick slices and brush with olive oil. Grill the bread over the coals until toasted. When the chicken is finished cooking, place it on top of the bread slices and let rest for 3 to 4 minutes (the bread will catch the juices).
To serve, spoon some of the tomato vinaigrette in the center of each plate and top with the chicken and bread. Garnish with the Pickled Tomatoes, purslane, onion blossoms and a drizzle of olive oil.
This recipe was provided by a chef, restaurant or culinary professional and may have been scaled down from a bulk recipe. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.
Combine the tomatoes and dill in a nonreactive bowl. In a saucepan, bring the vinegar, sugar, mustard seeds, salt, bay leaf and 1 cup water to a boil. Pour the vinegar mixture over the tomatoes and dill and let cool until ready to use.