Rhubarb Upside-Down Cake

1 1/4 c. butter, room temperature
1 lb. rhubarb, cut into 4 inch pieces
1 1/2 c. sugar
1/4 c. brown sugar
2 c. flour
1 1/4 t. baking powder
1/2 t. salt
1 t. lemon zest
1 t. vanilla
4 eggs
1/3 c. plain yogurt

Butter an 8 inch square pan and line with parchment paper.  Butter the parchment paper as well.  Toss the rhubarb, 1/2 c. of the sugar, and brown sugar in a bowl.  Layer the rhubarb in rows over the parchment paper in the bottom of the pan.  Add any remaining sugar from the bowl to the pan.  Beat the butter, remaining 1 c. of sugar, and lemon zest until light and fluffy.  Add the vanilla and eggs one at a time.  Stir in the yogurt at low speed.  Gradually add the flour, baking powder, and salt until combined.  Spoon the batter over the rhubarb in the pan.  Bake the cake at 375 degrees for 1 hour and 15 minutes.  Cool for 15 minutes before turning it upside-down on a serving plate.