Preheat oven to 350°F. Grease a springform pan (sides and all) with butter.
Pour the melted butter into the pan. Evenly sprinkle with brown sugar. Starting from the middle, place the figs cut side down in the pan, creating concentric circles of figs as you go outwards. Set aside.
In a standing mixer fitted with a paddle attachment, cream the butter and sugars until light and fluffy. Beat in the eggs, sour cream, whole milk, and vanilla extract.
In a separate bowl, combine flour, orange zest, baking powder, and salt. Slowly incorporate the dry ingredients into the wet, mixing until just combined.
Spread the batter evenly on top of the figs and bake for 1 hour. Allow to cool for at least 10 minutes before inverting over a cake tray. Devour!