Read more about unusual foods for the grill in Ellen Jackson’s “The universal grill.”

Steps

1. Put the olive oil in a small bowl with the garlic.
2. Remove the heel ends of the loaf and the crust, if desired. Use a serrated knife to cut the bread in 1-inch-thick slices. Cut the slices into 1-inch cubes. (The size and number of cubes should correspond roughly to that of the tomatoes.) Thread the bread cubes onto skewers and place them on a baking sheet. Lightly brush the bread on all sides with the garlic oil and sprinkle with salt.
3. Thread the tomatoes onto additional bamboo skewers, line them up with the bread on the baking sheet, brush with the garlic oil, and sprinkle with salt.
4. Add the 2 tablespoons olive oil to the remaining garlic-infused oil, or enough to make ⅓ cup total, and set aside.
5. In a separate bowl, add the leftover garlic to the white-wine vinegar with a pinch of salt and let sit for a few minutes. Whisk in the mustard, followed by the oil blend. Stir in the grated cheese and check the seasoning, adding salt and pepper to taste.
6. Preheat the grill to high. Grill the tomatoes, turning, until the skins brown and blister all over, 6 to 8 minutes. They should be charred and close to bursting. Add the bread to the grill halfway through, after 3 to 4 minutes. Grill the bread cubes, turning once or twice, until they are lightly toasty, 2 to 4 minutes.
7. Remove the bread and tomatoes from the skewers into a large bowl and toss with several tablespoons of the Parmesan vinaigrette. Continue adding vinaigrette until the items are sufficiently moistened. Add a few large handfuls of arugula leaves and some torn basil to make a salad.