Preheat oven to 400 degrees F.
Slice tomatoes in half horizontally and scoop out pulp and seeds. Salt insides and rest upside down on a sheet pan lined with a wire rack to extract juices, about 15 minutes. Meanwhile, in a medium bowl, mix together bread crumbs, garlic, basil, pepper, 1/4 cup of the grated Parmesan and oil. Stuff tomatoes with the filling, sprinkle with remaining Parmesan, and bake until tomatoes are cooked through and tops are golden brown, about 30 minutes.
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