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 granulated sugar (superfine is best (330 grams)); 1 Tablespoon baking powder; ¾ teaspoon salt; ¾ cup butter ((12 tablespoons) softened and room temperature); 4 egg whites (room temperature); 1 large egg (room temperature); 1 cup whole milk (room temperature); 2 teaspoons vanilla extract; 8 to 10 drops culinary lavender oil (about ⅛ teaspoon (see Notes)); 2 teaspoons dried culinary lavender buds (pulverized in a pestle or ground in a spice mill); 1 cup butter ( room temperature); 16 ounces cream cheese (room temperature); 5 to 6 cups powdered sugar ((565 to 678 grams)); 1 teaspoon vanilla extract; 2 to 5 drops culinary lavender oil (or to preferred taste-see Notes)