Make the cookies: Pulse the lavender in a spice or coffee grinder until finely ground. Remove 1/4 teaspoon to a small bowl; set aside for the glaze. Add 1/4 cup granulated sugar to the remaining lavender in the spice grinder and pulse until the sugar is fine.
Combine the butter, lavender sugar, the remaining 1/2 cup granulated sugar, the confectioners' sugar, salt and vanilla in a large bowl and beat with a mixer on medium-high speed until fluffy, about 2 minutes. Add the egg yolks and beat, scraping down the sides of the bowl, until combined, about 1 minute. Reduce the mixer speed to low; add the flour and beat until the dough comes together, 1 to 2 minutes.
Divide the dough between 2 large sheets of plastic wrap and roll each into a compact 10-inch log. Wrap each log in the plastic and refrigerate until very firm, at least 2 hours and up to 1 day.
Position racks in the upper and lower thirds of the oven and preheat to 350 degrees. Line 2 baking sheets with parchment paper. Unwrap one log of dough and slice into 3/8-inch-thick rounds. Arrange 2 inches apart on the prepared baking sheets.
Bake, switching the pans halfway through, until the cookies are golden around the edges, 20 to 24 minutes. Let cool 5 minutes on the pans, then transfer to racks to cool completely. Repeat with the remaining log of dough.
Make the glaze: Combine the white chocolate, half-and-half and the reserved 1/4 teaspoon ground lavender in a heatproof bowl set over a saucepan of simmering water (do not let the bowl touch the water); stir until melted, about 5 minutes. Remove the bowl from the saucepan and let sit until the glaze thickens slightly, 5 to 10 minutes. (If the glaze gets too thick to drizzle, reheat over the simmering water, stirring.) Drizzle the glaze over the cookies and top with sprinkles. Let set, about 2 hours.