Preheat the oven to 350 degrees F (175 degrees C). Grease and flour a 9 inch Bundt pan.
In a large bowl, cream together the butter, brown sugar and vanilla until light and fluffy. Beat in the egg until smooth. Combine the flour, baking soda, and baking powder; stir into the batter alternately with the yogurt. Spread the batter into the prepared pan.
Bake for 50 minutes in the preheated oven, until a knife inserted into the crown comes out clean.