4 ounces fresh mozzarella cheese, thinly sliced and chopped
½ cup small fresh basil leaves
Cook vinegar in a small saucepan over medium heat until thickened and reduced by half, 7 to 10 minutes. Set aside.
Heat ½ teaspoon oil in a large nonstick skillet or griddle over medium heat. Add 8 polenta slices; cook until golden brown on both sides, about 8 minutes, turning once halfway through cooking time. Repeat twice, using the remaining oil and the remaining polenta slices. Sprinkle the cooked polenta slices with salt.
Arrange 6 of the polenta slices on each plate. Layer with tomatoes, arranging the slices so they overlap slightly. Top with cheese and basil. Drizzle with the balsamic glaze.