Preheat oven to 500 degrees, with racks in upper and lower thirds. In a medium bowl, combine artichoke hearts, asparagus, and tomatoes. On a large piece of parchment paper, brush 1 dough half with artichoke-heart marinade and roll out to a 14-inch-long oval. Transfer dough on parchment to a rimmed baking sheet and top with half the vegetables, leaving a 1-inch border. Brush border with marinade and season pizza with salt and pepper. Repeat to make second pizza. Bake pizzas 10 minutes, rotating sheets halfway through. Sprinkle pizzas with cheese and bake until crust is deep golden and cheese is melted, 3 to 5 minutes.