Prepare the grill for direct cooking over medium heat, 350 to 450 degrees F.

Using 2 tablespoons of the oil, brush one side of each slice of bread.

In a medium bowl whisk the vinegar with the remaining 2 tablespoons oil and season with the salt and pepper. Set aside.

Brush the cooking grates clean. Grill the bread, oiled side down, over direct medium heat until lightly toasted and grill marks appear, about 1 minute. Remove from the grill.

Place a cast-iron griddle over direct medium heat, close the lide, and let it preheat for 2 to 3 minutes. Arrange the pancetta slices on the griddle in a single layer and cook until browned and crisp, 4 to 8 minutes. Turn pancetta ony once or twice and check frequently so that  it doesn’t burn. Transfer the pancetta to a sheet pan lined with paper towels.

Put two bread slices, toasted side up on each of four plates. Add the mixed greens to the medium bowl with the vinaigrette and toss to coat. Divide the greens equally among the eight slices of bread. Top with tomato slices, pancetta, and cheese, dividing them equally. Drizzle any remaining vinaigrette from the bowl over the sandwiches. Serve warm.