Preheat the oven to 350 degrees F. Grease a 8×8 inch square pan.
Combine the cake flour and baking powder in a small bowl. Set aside.In a larger bowl, cream the butter and ½ cup of sugar until light and fluffy, about 4-5 minutes. Add the egg yolks one at a time, beating until the mixture is pale and fluffy, another 3-4 minutes. Add the vanilla, almond extract, and lemon zest and beat just until combined. Fold in the almond flour.Beat the egg whites in a clean, dry bowl on medium high speed until foamy, then add the cream of tartar. Continue to beat until stiff peaks form.Fold in ⅓ of the egg whites, then ⅓ of the flour mixture. Repeat with the remaining egg whites and flour. Be very careful not to over-stir.Pour the batter into the prepared cake pan.Bake for about 30 minutes, or until a toothpick inserted into the middle of the cake comes out clean. Be careful not to over-bake.Remove the cake from the oven and let sit for 10 minutes. Carefully invert the cake.
While the cake is cooling, make the glaze: Combine the lemon juice and lavender flowersin a small saucepan or microwaveable dish, bring to a boil, remove and let steep for at least 5 minutes. Use a mesh sieve to strain the lavender flowers. Stir the powdered sugar and lavender liquid together until the sugar is dissolved.
Poke some small holes around the top of the cake with a toothpick to allow the glaze to fully absorb. Pour the glaze over the cake and let the cake sit for at least 20 minutes before serving.