Lavender Cake with Lavender Cream Cheese Icing

Name: Lavender Cake with Lavender Cream Cheese Icing
Prep time: 20 min
Cook time: 30 min
Total time: 50 min
Cuisine: American
Ingredients: 2-¾ cups cake flour ((300 grams)); 1-⅔ cups sugar (superfine is best (330 grams)); 1 Tablespoon baking powder; ¾ teaspoon sea salt; ¾ cup butter ((12 tablespoons) softened and room temperature); 4 large egg whites (room temperature); 1 whole large egg (room temperature); 1 cup whole milk (room temperature); 2 teaspoons vanilla extract; 8-10 drops lavender oil (about ⅛ teaspoon (see Notes)); 2 teaspoons culinary lavender buds (pulverized in a pestle or ground in a spice mill); 1 cup of butter (2 sticks, room temperature); 16 oz of cream cheese (2 packages, room temperature); 5 - 6 cups of powdered sugar ((565 to 678 grams)); 1 teaspoon of vanilla extract; 2-5 drops of culinary lavender oil (or to preferred taste-see Notes)