Drain artichoke hearts and place on paper towels to dry. Trim the tops and bottoms of carrots. Scrub. It is not necessary to peel these small carrots. Put carrots in a small saucepan and cover with water. Place over medium high heat and bring to a boil. Turn heat to medium and simmer for 5 minutes. Drain. Place the artichoke hearts and carrots into a bowl.

In a small bowl, mix 1 tablespoon olive oil and 1 tablespoon of the tarragon. Pour over the vegetables and mix to coat.
Place a sheet of parchment paper on a sided baking sheet. Spread the vegetables on the parchment paper. Place baking sheet in the oven for 15 minutes. Turn the vegetables and bake for an additional 15 minutes.

While vegetables are cooking, prepare the Parmesan Crisps. Combine the cheese and the tarragon in a small bowl, mixing toughly. Line two baking sheets with parchment paper. Spray paper with oil. Create 6 mounds of cheese on each sheet using 2 teaspoons of the cheese mix per mound. Once you have 12 mounds, flatten each into a 2” circle with the back of a spoon.

When you remove the vegetables from the oven, reduce the temperature to 300°. Immediately place the crisps in the oven. Bake until slightly browned, about 6-8 minutes. Remove from the oven. Slide the parchment paper onto a cooling rack. Using a wide spatula, immediately remove the crisps, placing two crisps on each of six serving plates. (Crisps will harden as they cool so work quickly.)

Evenly divide the artichoke hearts and the carrots between the six plates.

Combine the remaining olive oil and tarragon with the fresh lemon juice. Drizzle over the vegetables.