Preheat oven to 350 degrees. Beat granulated sugar, butter, and vanilla until well-blended.
Add egg and egg white, one at a time, beat well after each addition. Sift flour and combine with the baking powder, baking soda, and salt; stir well. Add the flour mixture to sugar mixture alternately with yogurt, beginning and ending with flour mixture. Stir in lavender. Pour the batter into a greased 9×5 inch loaf pan. Bake at 180 degrees for about 1 hour or until a sharp knife or cake tester inserted in the center comes out clean.
To prepare glaze, combine powdered sugar and remaining ingredients. Spread on the warm cake. Cool in pan 20 minutes on a wire rack before removing from the pan.