Glazed Lavender Sugar Cookies

Name: Glazed Lavender Sugar Cookies
Cook time: 2 h
Total time: 2 h
Cuisine: American
Ingredients: 4 cups (512 grams) all-purpose flour, plus more for dusting; 2 teaspoons dried culinary lavender, finely chopped or crushed in a mortar and pestle; 1 teaspoon baking powder; 3/4 teaspoon salt; 1 cup (227 grams) unsalted butter, softened; 2/3 cup (135 grams) granulated sugar; 2/3 cup (80 grams) powdered sugar; Zest from half of a lemon; 2 large eggs; 1 teaspoon vanilla extract; 3 cups (360 grams) powdered sugar; 1 cup (227 grams) unsalted butter, softened; Food coloring; 2 cups (240 grams) powdered sugar; 2 tablespoons (40 grams) corn syrup; 2 1/2 tablespoons whole milk; 1/2 teaspoon vanilla extract; Pinch of kosher salt; Food coloring, optional