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Preheat oven to 350 degrees. Butter a 2-quart shallow baking dish or a deep pie plate; set aside.
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Place tomato wedges in a large bowl; sprinkle with cornstarch and season with salt and pepper. Toss gently to combine.
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Place flour, cornmeal, baking powder, baking soda, and 1 teaspoon salt in the bowl of a food processor; pulse to combine. Add butter and pulse until mixture looks like coarse breadcrumbs. Add egg and buttermilk, pulse a few more times until mixture comes together. If the mixture is too liquid, add more flour, a spoonful at a time. If mixture is too dry, add a few drops of buttermilk.
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Gently toss tomato mixture again and spread it over the bottom of the prepared baking dish. Drop spoonfuls of the flour mixture on top, spreading evenly with a knife, leaving some gaps so that steam can escape. Transfer cobbler to oven and bake until golden and bubbling, 45 to 60 minutes. Let cool slightly before serving.