Preheat the oven to 400 degrees. Line a sheet pan with parchment paper.
In the bowl of an electric mixer fit with the paddle attachment, mix flour, sugar, baking powder, salt and lavender. Add the cold grated butter and mix at the lowest speed until the butter is mostly combined and the dough looks craggy, about 20-30 seconds.
Mix the egg, ½ cup of heavy cream and vanilla in a small bowl. With the mixer on low speed, slowly add the wet ingredients to the flour and butter mixture. Mix until just blended, about 30 seconds to 1 minute. The dough will look lumpy and may not be fully incorporated yet!
Dump the dough onto a floured surface and use your hands to form it into a disc pressing any dry ingredients into the dough to combine. If the dough seems too dry you can add more heavy cream to help bring it together. Shape the dough into a circle, about 1-inch thick. You should still see small pieces of butter in the dough. Slice the circle into 8 wedges. Place the scones onto the prepared sheet pan.
Place the sheet pan with the scones into the freezer for 30 minutes. After chilling, brush the tops of the scones with the remaining 1 tablespoon of cream and sprinkle with sugar if desired. Bake for about 12-14 minutes, until the bottoms are golden brown and the scones look set. Let the scones cool completely and then pour the glaze onto the scones.