Place a rack at the top of the oven and preheat the oven to 400 degrees F.
Cut 1/4-inch off the top of each tomato and discard. Use a spoon to hollow out the tomatoes to about halfway down the center. Discard the pulp or reserve for another use. Use your hands to rub the outside of the tomatoes with a light coating of the oil, then drizzle any remaining oil inside the tomatoes. Season the inside of the tomatoes with 3/4 teaspoon salt and 1/4 teaspoon pepper. Place the tomatoes in a 9-by-13-inch baking dish and reserve.
In a medium bowl, stir together the oats, flour, scallions, lemon zest, cheese, 1/2 teaspoon salt and 1/4 teaspoon pepper. Use your fingers to work the butter into the mixture until it resembles large crumb-like pieces. Evenly divide the oat crumble among the tomatoes.
Bake until the tomatoes are tender and the crumble is golden brown and crispy, 45 to 50 minutes, rotating the dish halfway through.
Carefully transfer the tomatoes to a platter and garnish with the sliced basil leaves to serve.
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