Preheat oven to 350°F Line a 9x13-inch baking pan with foil and grease.
Beat brown sugar and oil until combined. Add eggs one at a time, beating well after each addition. Beat in yogurt, mashed bananas and vanilla. Add next 3 ingredients and mix until combined. Pour batter into prepared pan. Bake in preheated oven 30-35 minutes, or until a toothpick inserted in the center comes out clean.
Remove from oven and using a long wooden skewer, poke holes all over the surface of the cake.
Spread caramel topping over surface of cake. As it cools, it will absorb through the holes in the cake. Let cool and serve.