Heat broiler, with rack 4 inches from heat. Place red pepper, skin side up, on one end of a large rimmed baking sheet; place half the tomatoes on the other. Broil until pepper is charred, 8 to 10 minutes. Let cool slightly, then peel pepper with a paring knife.
In two batches, puree broiled pepper and tomatoes, remaining tomatoes, tomato juice, and 1 tablespoon oil in a blender until very smooth, about 3 minutes. Season with salt and pepper. (To store, refrigerate, up to 1 day.)
In a small bowl, combine goat cheese, 1 tablespoon oil, and lemon zest; season with salt and pepper. Spread wraps with goat cheese mixture, then top with ham and arugula. Roll up wraps. (To store, wrap tightly in plastic or waxed paper and refrigerate, up to 1 day.)
Broiling the bell pepper and half of the tomatoes gives this twist on gazpacho a deeper, more intense flavor. It's delicious cold or at room temperature. We made these sandwiches with lavash wraps, which are thicker and chewier than tortilla-style versions. Either variety will work -- you'll find both in the bread aisle.