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Heat oven to 425 degrees and line a rimmed baking sheet with parchment paper. Remove pizza dough from refrigerator and allow to sit at room temperature while you prepare the tomatoes.
In a mixing bowl, combine cherry tomatoes, olive oil, rosemary sprigs, a generous pinch of salt, and pepper, tossing to coat. Spread mixture on prepared baking sheet in a single layer. Roast on center rack until skins burst and tomatoes begin to shrivel, about 12 to 15 minutes. Remove from oven, transfer to heatproof bowl, and lightly crush tomatoes with a potato masher or fork. Discard rosemary sprigs.
Increase oven to 450 degrees with rack in lowest position. Pour about 1 tablespoon olive oil onto a rimmed baking sheet; place dough on sheet and coat on all sides with oil. Stretch dough to create a large rectangle, roughly the size of your sheet. (If dough will not stretch, allow it to rest for another 5 to 10 minutes before trying again.)
Spread cherry tomato mixture evenly over dough, leaving a ½-inch border. Top with cheese and sprinkle with rosemary. Bake until crust is golden and cheese is melted and lightly browned, about 20 to 25 minutes. If crust begins to get too dark, move pizza to center oven rack and reduce temperature to 400. Remove from oven and sprinkle with sea salt and a drizzle of olive oil. Let pizza rest 5 minutes before slicing.