In a small saucepan, bring the balsamic vinegar, sugar and thyme to a boil over medium heat. Reduce to a simmer and let cook until the liquid is reduced by a third, about 15 minutes. Remove from heat, discard the thyme and let it cool.

On a serving plate, arrange the sliced mozzarella, top with strawberries and drizzle with the balsamic sauce. Serve cold or at room temperature.