Preheat oven to 350 degrees F (175 degrees C). Grease a 9-inch baking pan with butter; dust with flour, shaking off excess.
Beat 2 cups sugar, oil, and eggs with an electric mixer until creamy. Beat in milk. Add 2 cups flour and baking powder; beat until batter is smooth.
Combine 3/4 cup sugar and water in a small saucepan. Simmer until sugar dissolves and syrup is clear and thick, 15 to 20 minutes.
Pour syrup into prepared baking pan. Arrange banana halves on top. Pour batter over bananas.
Bake cake in the preheated oven until top is golden brown and a toothpick inserted into the center comes out clean, about 40 minutes. Let cool for 10 minutes before inverting onto a platter.