Preheat your to 450 degrees F and open the flame broiler.
Cut the lemons in half and sear over the flame broiler until charred.
Turn down your to "Smoke" mode, and combine 1/2 cup sugar and 1/2 cup water in an aluminum pan. Smoke for about 45 minutes, or until the mixture becomes a thick, simple syrup.
While the simple syrup is smoking, juice the lemons into a juice container. Be sure to remove all seeds by straining the juice if need be.
Pour the simple syrup into the lemon juice, add 2 cups of sugar and about half the bottle of sparkling water (or enough to fill the juice container up completely). Stir until the sugar has dissolved. Add ice and garnish with mint and thyme leaves.