Bring a pot of water to a boil. Fill a large bowl with ice water. In a medium bowl mix vinegar, agave, salt, pepper, garlic and basil.
Drop carrots into boiling water for 2-3 minutes and remove, placing immediately into ice water. Drain carrots and put them into the marinade for about 20 minutes.
Preheat oven to 425 degrees. Take pizza crust out of freezer.
In a small bowl mix the olive oil, salt and pepper. Brush olive oil mixture on the crust and place crust on the rack or a heated pizza stone and cook for 7 minutes.
Take the crust out of the oven and spread tomato sauce over it. Cover with the mozzarella. Take carrots out of the marinade and dry in a towel.
Place carrots however you like around the pizza. Cook for another 20 minutes. Take out and serve. Top with some more fresh basil if you like.
To save time, you can skip the instructions to boil the carrots and put them in ice water. Instead put them directly into the marinade after you slice them.