Cream butter with brown sugar until light; beat in egg and vanilla.
Into another bowl, sift together the flour, soda, baking powder, and salt. Add to the creamed mixture alternately with the yogurt. Mix well and pour batter into a greased and floured 9-inch tube pan. Bake at 350° for 45 to 55 minutes, or until a wooden pick or cake tester inserted in center comes out clean.
Cool slightly; remove from pan. Sprinkle with powdered sugar and serve warm or cool.