In a small saucepan, add the balsamic vinegar. Heat over low, stirring occasionally, until thick and reduced by at at least 2/3. The vinegar should easily coat the back of a spoon. Remove from heat and set aside.
Preheat the oven to 375 degrees F. Line a large baking sheet with foil or parchment paper. Brush the bread with olive oil on both sides and season with salt and black pepper. Place the bread in the oven to toast, about 8-10 minutes (flip after 5 minutes).
Divide the burrata between two bowls. Distribute the figs evenly and drizzle with reduced balsamic vinegar. Serve with crispy bread and enjoy immediately!