Preheat oven to broil.
Brush olive oil on sliced baguette and place on a racked sheet tray. Toast in the oven for 3-4 minutes, or until lightly golden brown on both sides.
In a small saucepan, reduce the balsamic vinegar with 1 1/2 tablespoons honey, stirring constantly with a wooden spoon, until syrupy and just starting to froth up, about 5 minutes. Take off of heat immediately.
Place 3 slices of cheese on each slice of toasted baguette, top with 3-4 slices of fig, and return to the oven for 5 more minutes, until the cheese is melted.
Drizzle each piece of tartine generously with the balsamic syrup and the remaining honey. Top with fresh thyme leaves and serve immediately.