Heat a skillet over medium-high heat. Lightly spread butter over one side each of the sandwich bread and lay the buttered side down on the skillet. Top with sliced mozzarella. (You can add the mozzarella to one or both slices. I prefer both slices so that the strawberries and arugula with both stick to the melted cheese).

While the cheese is melting, toss the arugula in a small bowl with the oil and vinegar. Add a generous grind of black pepper.

Once the cheese is melted and the bread is grilled, add the strawberries to one slice of bread and the arugula to the other, then close the sandwich and serve!