Preheat panini press or indoor grill to medium-high.
Spread 1½ tablespoons of pesto on each of 2 slices. Top pesto with 1 ounce of mozzarella, sliced tomato, and another ounce of mozzarella. Top with a second slice of bread.
Mist press or griddle with olive oil and place sandwich on the heated surface, allowing to brown for 4-5 minutes; flip and allow to brown on the other side, about 3-4 minutes. Serve hot.