Combine cornstarch, flour, baking powder, baking soda, and salt in a bowl, whisk gently and set aside. In a mini-food processor, or spice grinder, grind 1/3 cup sugar with the dried lavender until lavender is a fine powder evenly distributed in the sugar. If you do not have a food processor or spice grinder, use a mortar and pestle or mince lavender flowers by hand.
Place lavender sugar, remaining 1/3 cup sugar, and butter into the bowl of a stand mixer fitted with a paddle attachment. Mix on medium speed for 1 minute, stop the mixer and scrape down the sides of the bowl with a rubber spatula. Continue mixing for 2 more minutes. The mixture should be light in color and fluffy.
Add the egg yolks and vanilla and mix until combined, about 30 seconds. Stop the mixer and scrape down the sides of the bowl. On low speed, slowly add the reserved flour mixture and mix until the dough starts to come together. It will look like dry sand at first. Add 1 tablespoon of water and continue to mix until the dough starts to clump together and form a ball of dough. If necessary, add 1 additional tablespoon of water. Dough is finished once it forms a ball.
Cut the dough into four pieces of roughly the same size. Place each on a sheet of plastic wrap and flatten into a small disk. Wrap tightly and refrigerate until firm, about 1 hour.
Preheat oven to 350 F and place oven rack in middle of oven to ensure even heating. Line three baking sheets with parchment paper and set aside.
Remove dough from refrigerator, unwrap it and place on a lightly floured work surface. Lightly flour the top of dough. Roll to 1/4-inch thick (dough will crack but can be easily patched back together). Stamp out rounds as closely as you can, without overlapping them, using a plain or fluted 1-inch round cutter, rerolling the dough as necessary until it is all used.
Place cookies on prepared baking sheets, 15 to 20 per sheet and at least 1/2-inch apart. Bake one sheet at a time until cookies are firm and pale on top, and golden on bottom, 9 to 11 minutes. Remove from oven and cool completely.
Flip half the cookies upside down and gently spread about two teaspoons of dulce de leche on each. Place a second cookie on top and gently press to create a sandwich. Brush lightly with a little honey and put 2 to 3 lavender flowers on top for garnish. Dust generously with powdered sugar before serving.