Get your grill nice and hot, or heat up a grill pan over medium-high heat. Spread a 1/4 Tbsp of olive oil onto one side of each slice of bread. Place the slices of bread, olive oil-side down, onto the grill or grill pan. As the bread is grilling, spread a 1/4 Tbsp of olive oil onto the face-up sides of the bread slices. Grill the slices of bread approximately 2 minutes per side, or until each side is golden brown and slightly charred. Remove from heat.

I like to get nice black grill marks on mine, so I cook mine just a little bit longer.

Place 2 of the 4 slices of bread on a lined baking sheet. Evenly distribute the mozzarella between the two slices and place the baking sheet in the oven under the broiler (on high). Watch closely until the mozzarella is melted and starting to brown on top, about 3 to 4 minutes. Remove pan from broiler.

Add 2 to 3 slices of tomato on top of the melted mozzarella on each slice. Sprinkle salt and pepper evenly over the tomato layer. Top each sandwich half with the leaves of basil and then drizzle with balsamic vinegar. Place the two remaining grilled slices of bread on top. Serve immediately.