01 - Preheat oven to 350°F. Grease and flour an 8-inch round cake pan.
02 - Whisk together flour, baking powder, and salt in a bowl. Set aside.
03 - Beat softened butter and granulated sugar in a large bowl until light and fluffy. Add eggs one at a time, mixing well after each addition. Blend in lavender and vanilla extract.
04 - Alternate adding flour mixture and milk to the butter mixture, beginning and ending with flour. Mix until just combined.
05 - Pour batter into prepared pan and smooth top. Bake for 25-30 minutes until a toothpick inserted in center comes out clean.
06 - Simmer water, sugar, and lavender buds in a small saucepan for 3 minutes. Strain and set aside.
07 - Let cake cool in pan for 10 minutes. Poke small holes in surface and brush lightly with warm lavender syrup. Cool completely.
08 - Mix powdered sugar, lemon juice, and chopped lavender until smooth. Drizzle over cooled cake and let set before slicing.