Preheat an outdoor grill for medium heat and lightly oil the grate.
Lay bacon slices on the hot grill; cook until brown on the bottom, about 2 minutes. Flip and cook 1 minute more. Transfer to a plate.
Tear arugula into bite-sized pieces and arrange over the bacon. Scatter tomatoes and Parmesan cheese on top. Drizzle very lightly with olive oil and a few drops of balsamic vinegar. Season with salt and pepper. Serve immediately.
