In a small saucepan, heat the dried figs, bourbon, water, and tiny pinch of salt over medium low heat for about 15 minutes. Mixture is ready when the figs are soft and most of the liquid has evaporated (if you want to measure, there should be 1/2 cup of liquid left).
Place mixture into a blender and blend until smooth. Allow to cool slightly while you make your banana bread batter.
In a small saucepan, heat the butter over low heat for roughly 5 minutes, swirling the pan every 20 seconds or so. Heat until the milk solids turn a light golden brown color. Remove from heat and allow to cool slightly.
In a large bowl, mix together brown sugar, mashed bananas, and brown butter. After mixing, stir in eggs, yogurt, milk, and vanilla.
In a separate bowl, whisk both flours, baking soda, and salt. Fold gently into batter until just combined.
Pour half of batter into loaf pan and top with half of bourbon fig mixture. Try to place it evenly over the batter, and do not swirl (yet!). Top with remaining banana bread batter. This time, scoop small dollops of the remaining bourbon fig spread over the batter. Use a knife to gently swirl everything together.
Bake for 1 hour, or until a knife inserted in the center of the loaf comes out clean. Allow to cool slightly before devouring.