Char peppers over gas flame or in broiler until blackened on all sides. Enclose in paper bag 10 minutes.
Peel and seed peppers. Transfer peppers to blender and puree until very smooth. Season to taste with salt. (Coulis can be made 1 day ahead. Cover and refrigerate. Bring to room temperature before serving.).
Roll out pastry sheet on floured surface to 1/8-inch thick square. Trim edges to form 11-inch diameter round. Transfer to 9-inch tart pan with removable bottom. Fold in overhang to form double-thick sides. Pierce pastry with fork. Cover and chill 1 hour. (Can be prepared 1 day ahead. Keep refrigerated.).
Preheat oven to 425°F Line pastry with foil; fill with pie weights or dried beans. Bake crust until sides are set, about 20 minutes. Remove foil and beans. Bake crust until bottom is golden brown, pressing with back of fork if bubbles form, about 8 minutes. Transfer tart to rack. Reduce oven temperature to 325°F.
Whisk eggs, cream, Parmesan cheese, and salt and black pepper in medium bowl to blend. Pour egg mixture into hot tart crust. Bake tart until custard is set, 30-40 minutes. Cool slightly.
Toss arugula with oil and lemon juice in large bowl. Season with salt and pepper.
Cut tart into wedges; drizzle with coulis. Serve warm with arugula salad.