Spread pine nuts on a cookie sheet and toast under broiler for 1-3 minutes, stirring occasionally.
Add olives, garlic, pesto and pine nuts to food processor. Pulse until chopped fine.
With the food processor running, slowly add olive oil. Set tapenade aside.
If you do not have a panini press preheat a grill pan over medium heat for 1-2 minutes. (Droplets of water should just sizzle when flicked onto pan.)
Toss tomatoes, 1 tbsp. oil, salt and pepper together.
Place tomatoes cut side up in pan, cover with fresh aluminum foil and weigh down with heavy skillet or pan. Cook until tomatoes are softened and browned on first side, about 4 minutes.
Transfer tomatoes to a plate and wipe pan clean.
Spread olive tapenade evenly over one side of each slice of bread.
Assemble two sandwiches by layering ingredients as follows between prepared bread, with olive tapenade on the inside of sandwich: half of mozzarella, cooked tomatoes, basil, and remaining mozzarella. Press gently on sandwiches to set.
Reheat the pan over medium-high heat for about 1 minute. Brush the outside of sandwiches lightly with remaining olive oil. Place sandwiches in pan and weigh down with a heavy skillet or Dutch oven. Cook sandwiches until bread is golden brown and crisp on both sides and cheese is melted, about 3-4 minutes per side. Serve and enjoy!