Preheat oven to 350°.
In a small saucepan, melt 1/4 c. butter over medium heat.
Stir in 3/4 c. brown sugar.
Pour mixture into 9 inch round pan.
Place pineapple rings on top of brown sugar and place a maraschino cherry in the center of each ring.
In a medium mixing bowl, cream 1/4 c. butter, 1/2 c. granulated sugar, and 1/4 c. brown sugar.
Add sour cream, milk, egg, pineapple juice, and vanilla. Mix until blended.
Use a food processor to grind reserved pineapple rings (or chop finely) and stir into batter.
Stir in flour and baking powder just until moistened.
Pour batter over pineapple rings in pan; spread evenly.
Bake at 350° 50-55 minutes or until top is golden brown and edges begin separating from pan.
Use a knife to loosen edges; cool 10 minutes on a wire rack.
Place a serving plate on top of pan and invert cake onto the plate.