Brush the bread on both sides with olive oil and season with salt and pepper. Place on a baking sheet and set aside. Coat the chicken well with the fennel spice and set aside until ready to cook.

Prepare the grill and let it burn down to medium-hot coals. Place the bread on the grill, away from direct heat, and grill on both sides until brown and crispy on the outside but still soft within, about 5 minutes.

Leave the mushrooms whole, and toss in a bowl with 1/2 cup of the olive oil, 1 teaspoon of the thyme, the garlic, and salt and pepper to taste. Immediately grill the mushrooms (be careful not to allow the flames to flare up and burn the mushrooms), turning at least once, until browned and cooked through, about 5 minutes. As the mushrooms are done, return them to the marinade in the bowl. Let cool, finely chop, and return to the marinade.

Add the shallot, vinegar, parsley, the remaining 1 teaspoon thyme, and salt and pepper to taste, to the mushrooms. Toss well and add the remaining 1/4 cup olive oil, if necessary, for balance. Toss well again. (The mushroom vinaigrette may be made a day ahead, covered, and refrigerated, and then returned to room temperature before serving.)

When the coals have burned down to a medium fire, place the chicken, skin side down, on the grill and cook until browned, about 2 minutes. Turn over, move to the edge of the grill away from direct heat, and continue to cook until opaque throughout, about 7 minutes. Remove to a plate.

In a bowl, toss the arugula with the citrus vinaigrette. Place a grilled bread slice on each of 4 plates. Slice the chicken breasts crosswise and arrange on top of the bread. Pour any accumulated chicken juices into the mushrooms and stir. Spoon the mushrooms over and alongside the chicken. Divide the arugula among the plates. Serve immediately.