Assemble sandwich by smearing insides of bread slices with pesto. Arrange a layer of sliced tomato and season with a few turns of fresh pepper. Layer the mozzarella slices over the top and then place another piece of bread on top to make the sandwich. Drizzle olive oil over skillet's surface and place sandwiches on the hot skillet or panini press. If using a skillet, place another heavy skillet over the top to form a "press". Turn after 2 to 3 minutes and replace weight. The sandwich is ready when golden brown and mozzarella has melted around the edges.
Toast pine nuts in a skillet over medium heat until fragrant, about 5 minutes. Combine pesto ingredients in a food processor and pulse until well combined but still rough-textured. If you have a panini press, turn it on to warm up; otherwise, set a cast iron skillet over medium heat.