Preheat oven to 425 degrees (F) and line baking sheet with parchment paper.

Put sugar and lavender in a food processor fitted with a steel blade attachment and pulse 10 times until the lavender is ground up. Pour the sugar through a sieve into a bowl and return to the food processor. Discard the lavender husks left behind. Add the flour, baking powder, lemon zest, xanthan if using, and salt and pulse to combine. Add the butter and pulse until it is roughly the size of peas.

Whisk the eggs and heavy cream together in a bowl. Add to the food processor and pulse just until everything comes together. It should be a little crumbly still.

Pour mixture out onto the prepared baking sheet and pat into a disk that is about 1½ inches thick. Cut into 6 triangles and using a spatula, evenly space the scones on the baking sheet. Brush each scone with heavy cream and sprinkle with additional sugar if desired.

Bake for 14-16 minutes, or until the scones are lightly golden brown.

Remove from oven and leave on the pan to cool completely.

Make the glaze. Whisk the powdered sugar, lemon juice and salt together in a bowl. It should be thin enough to pour from a spoon but not too runny. Pour the glaze into a sandwich bag and seal. Snip off one corner and drizzle glaze over scones. Garnish with some more lavender if desired.

Scones can be kept at room temperature and are best if eaten within a day or two.