Preheat the oven to 325°F. Do not grease a tube pan.

In a large bowl, sift together the cake flour, 1 1/4 cups sugar, baking powder, and salt. Set aside.

In another large bowl, whisk together the egg yolks, oil, water, lemon zest, lemon juice, and chopped mint.

Add the dry ingredients to the wet ingredients and whisk until smooth.

In a separate bowl, beat the egg whites with the cream of tartar until soft peaks form.

Slowly add the remaining 1/4 cup sugar and continue beating until stiff peaks form.

Gently fold the egg whites into the batter in 3 additions, being careful to keep the batter airy.

Pour the batter into the tube pan and bake for 50 to 60 minutes, or until a skewer inserted into the center comes out clean.

Invert the pan and cool the cake upside down completely before releasing it from the pan.

To make the glaze, whisk together the powdered sugar, lemon juice, and warm water until smooth.

Drizzle the glaze over the cooled cake, then sprinkle the crushed lavender over the top.

Slice and serve.