Preheat the oven to 450°F. Lay the tomato slices on a paper towel–lined plate and sprinkle with ¼ teaspoon of the salt. Top with more paper towels and set aside.
Stretch the dough into a 16-by-10-inch oval on a clean surface sprinkled with cornmeal. (If the dough pulls back, let it rest 15 minutes.) Transfer to a parchment-lined baking sheet. Set aside.
Cook the bacon over medium heat in a nonstick skillet until crispy. Transfer to a paper towel–lined plate, reserving 2 tablespoons of the drippings in the skillet. Reduce heat to low and add the shallot, garlic, pepper, and the remaining salt. Cook 1 minute. Whisk in the vinegar. Brush 2 tablespoons of the vinaigrette over the dough.
Bake the dough until it is brown, 8 to 10 minutes. Top with the tomatoes, bacon (broken into pieces), and mozzarella. Return to oven and bake until the cheese is melted and beginning to brown, about 10 minutes more. Toss the greens with the remaining vinaigrette and serve over the flatbread.
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