Combine brown rice and pesto, stirring to evenly distribute. Spread into the bottom of a large, oven-proof skillet. Arrange tomato halves, cut side down, and mozzarella over top and season with salt and a drizzle of olive oil. Place under broiler until cheese is melted, about five minutes.
As skillet is cooking, heat balsamic vinegar over high heat in a medium pan. Reduce by half and let cool. Garnish skillet with fresh basil and drizzle with balsamic reduction.
Broil, Assemble, Stovetop