"A deliciously simple shortbread made with Meyer lemons, and topped with a homemade lavender flower and Meyer lemon glaze. This is an adapted recipe from several I've found over the years, which I combined and perfected from my Grandma's lemon shortbread."
Beat butter, 1/4 cup confectioners' sugar, white sugar, lemon zest, and salt together in a bowl with an electric mixer until fluffy. Gradually sift flour into batter, stirring in each addition; add 3/4 teaspoon lemon juice. Gently knead until dough holds together. Press dough into an 8x8-inch pan.
Bake in the preheated oven until shortbread is lightly browned around the edges, 30 to 40 minutes. Cool in pan to lukewarm temperature and transfer to a wire rack to cool completely.
Warm milk in a saucepan over medium heat; cook, stirring constantly, until milk begin to boil. Remove from heat and add lavender flowers. Cover pan and steep until fragrant, 6 to 10 minutes. Strain and discard flowers. Gradually whisk 1 cup confectioners' sugar, 1 tablespoon at a time, alternating with 1 tablespoon Meyer lemon juice, until glaze is smooth and opaque. Spread over cooled shortbread. Refrigerate to allow glaze to harden, about 30 minutes.
If you are using salted butter, then simply omit the salt in the dough. I highly recommend using the squeezed juice straight from the lemon...it tastes much better. If you do not want to use milk in the glaze, water works just as well with the obvious varying of the flavor.
If the dough is too moist, add a little bit of flour. If the dough is too dry, add a little bit more lemon juice.