1. Preheat broiler.
2. Toss tomatoes and artichokes with 1 teaspoon oil, and arrange in a shallow baking pan. Broil, stirring occasionally, about 4 minutes or until charred and tomatoes are wilted.
3. Preheat oven to 450°. Top each flatbread with half of tomatoes and artichokes. Sprinkle with grated Parmesan; bake in bottom third of oven 10 minutes or until golden brown and crisp.
4. While the pizza is baking, toss the arugula with shaved Parmesan, lemon juice, remaining 1 teaspoon olive oil, salt, and pepper.
5. Cut pizza into wedges, and serve with arugula alongside.