Preheat oven to 350°F or 176°C . Line a baking sheet with parchment paper.
Combine flour and cornstarch in a large bowl and set aside.
In a small bowl create a lavender lemon sugar by combining your sugar, lavender, lemon zest and vanilla extract. Set aside.
In a small bowl, whisk together your egg and cold buttermilk.
Grate your frozen butter into your flour mixture an use a pastry cutter (or your fingers) to combine until they're crumbly, pea sized pieces.
Make a well in the center of your dough and whisk in your egg and buttermilk. Also add in your lavender lemon sugar. Combine until a thick dough forms, using your hands to gently kneed until dough is crumbly, but easy to manage.
Place your dough onto your parchment lined baking sheet, pat into an 8-inch circle, and cut into 8 wedges with a sharp knife. Brush with your 2 tablespoons buttermilk.
Arrange the wedges around the baking sheet, leaving room for rising and expansion while they bake.
Bake for 30 minutes, or until golden brown. Cool on a wire rack. Make your icing while your scones bake.
Optional icing: Add the powdered sugar, lemon juice, and vanilla extract to a small bowl and stir until combined. Drizzle over scones after scones have cooled for a few minutes.