Preheat the oven to 425 degrees F.
Dust a clean work surface with flour. Lay 1 sheet of puff pastry on the dusted work surface and dust with a pinch of lavender. Gently press the lavender into the puff pastry using a rolling pin, dusting with flour, if necessary. Coat half of the puff pastry with egg wash using a pastry brush and fold it over the non-egg washed half, forming a horizontal seam. Brush the exposed puff pastry with egg wash, and sprinkle with salt. Fold the puff pastry again, forming a horizontal seam. Coat the exposed puff pastry with egg wash, and sprinkle with lavender and turbinado sugar. Using a sharp knife, trim the edges of the rectangle to make a uniform rectangle with exposed edges, rather than folded seams. Using a 3 inch ring cutter, cut out the center.
Arrange the rectangle and cut out circle of puff pastry separately, but next to one another, on a parchment lined baking sheet.
Bake until puffed and deeply golden brown, about 35 minutes.
Fill the center with vanilla ice cream and serve immediately.