TO ROAST THE RADICCHIO: Adjust the oven rack to the middle position, and preheat the oven to 400 degrees.

Cut each radicchio half into 5 wedges. In a cast-iron or other oven proof 10-inch skillet, combine 2 tablespoons of the olive oil and 2 teaspoons of the vinegar. Arrange the wedges of radicchio in the skillet in a concentric circle, and place a small piece of rosemary underneath and on top of each wedge.

Drizzle the remaining olive oil and vinegar over the radicchio, and sprinkle over the salt. Cover with plastic wrap and then foil, and roast in the oven for 15 minutes. Remove the foil, puncture the plastic to allow the steam to escape, and remove the plastic.

Turn the wedges of radicchio over, and on the stovetop, over medium heat, cook the radicchio about 3–5 minutes to caramelize slightly, being careful not to burn it.

TO SOAK THE MOZZARELLA: Bring it to room temperature and slice into ½-inch-thick slices. Pour warm salted water over the cheese to cover, and allow to sit a few minutes, until softened. Drain the slices on paper towels.

Grill the bread (see Notes, below). Rub one side of each slice of bread with the garlic clove, and cut each slice in half on the diagonal. Place the slices on serving plates, garlic side up.

FOR THE PESTO: Preheat the oven to 325 degrees.

Spread the pine nuts on a baking sheet, and toast in the oven for about 8-10 mnutes, until lightly browned.

using a mortar and pestle, pulverize the pine nuts, garlic, basil, and salt into a smooth paste. (If you don't have one, finely chop the ingredients and smash them with a knife to puree.) Slowly drizzle in the olive oil, and add the Parmesan, mixing well to incorporate. Season with lemon juice and salt to taste, just before serving.

TO ASSEMBLE THE SANDWICHES: Arrange 2 or 3 slices of mozzarella over each half-slice of bread, and spoon about a tablespoon of pesto over the cheese. Arrange the radicchio over the pesto and drizzle with olive oil.