Preheat oven to 375°F. Set frozen puff pastry on counter to thaw.
Sauté onions in olive oil over medium heat until translucent/slightly browned. Add brown sugar, balsamic vinegar, and butter. Mix to combine.
Reduce heat to medium-low and cook for approx. 20-25 minutes until onions are fully caramelized, stirring occasionally. Remove from heat.
On floured surface, slightly roll out puff pastry and cut each sheet into 9 square pieces. Place the squares, not touching, onto two baking sheets.
Crumble half the goat cheese onto the puff pastry. Layer the caramelized onions over the cheese. Place 3-4 fig slices on top and then crumble remaining cheese over the figs.
Bake in preheated oven for ~20 minutes. Remove baking sheets and drizzle honey over each pastry square.
Return baking sheets back to the oven for an additional 10-15 minutes, or until the tarts are golden brown. Let cool slightly and enjoy!