Preheat oven to 350 degrees. Grease an 8 inch square baking dish.
In a bowl, mix together the flour, baking powder and salt. Set aside.
In a mixing bowl, using an electric mixer, beat the butter until creamy. Beat in ⅔ cup of the sugar and beat for 1 minute, scraping side of bowl. Stir in the egg and beat for about 30 seconds, scraping side of bowl, then beat in cinnamon and vanilla.
Add the flour mixture and the milk alternately to the batter, stirring until blended.
Spread the chopped rhubarb in the bottom of the baking dish and toss with the remaining ⅔ cup of sugar. Spread the batter over the top of the rhubarb. It may not go all the way to the sides.
Bake the pudding cake for 45 minutes or until a skewer inserted comes out with moist crumbs.