-
Preheat a grill pan or nonstick skillet over medium heat.
-
Layer the bread with slices of proscuitto, basil leaves, and sliced mozzarella.
-
Coat the grill pan with 1 Tbsp butter or oil.
-
Place the sandwiches in the pan and cook until the bottom is golden brown, 2-4 minutes.
-
Remove the sandwiches to a plate and add more butter to the pan; return the sandwiches to the pan, browned-side-up, and cook until golden brown on the other side and the cheese is melted, 2-4 minutes.
-
While the sandwiches cook, juice the lemons into a large bowl. Whisk in the vinegar, oil, salt, and honey.
-
Use a vegetable peeler to shave the Parmesan into strips.
-
Add the arugula and shaved Parmesan to the bowl with the dressing and toss to combine.
-
Serve the salad alongside the sandwiches.