Reheat the oven to 350 degrees F. Oil 8 standard size ramekins, place on a baking sheet and set aside.
For the Topping: In a small saucepan melt the butter and mix in the brown sugar. Divide the mixture evenly among the the prepared ramekins. Place several piece of fig in each ramekin and set aside.
For the Cake: In a medium mixing bowl add the flour, baking powder and salt. Place near your work station.
In the bowl of an electric mixer, such as a KitchenAid, fitted with a paddle attachment, add the butter and sugar and beat well until combined. Add the eggs, one at a time, scrapping down the sides as needed. Mix in the vanilla. Slowly add the flour mixture and milk alternating as you go. Mix well.
Pour the batter into the ramekins. Place in the oven and bake until firm or a cake tester inserted comes out clean, about 45 minutes. Remove the cakes from the oven and allow to cool for about 10 minutes before inverting and serving. Top with a generous dollop of vanilla ice cream.