Preheat oven to 350°.
To prepare cake, beat granulated sugar, butter, and 1/2 teaspoon vanilla at medium speed of a mixer until well-blended (about 5 minutes). Add egg and egg white, 1 at a time; beat well after each addition. Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking powder, baking soda, and salt; stir well. Add flour mixture to sugar mixture alternately with yogurt, beginning and ending with flour mixture. Stir in lavender.
Pour the batter into an 8-inch loaf pan coated with cooking spray. Bake at 350° for 1 hour or until a wooden pick inserted in center comes out clean.
To prepare glaze, combine powdered sugar and remaining ingredients. Spread over hot cake. Cool in pan 20 minutes on a wire rack; remove from pan. Cool completely on wire rack.