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1
Adjust one oven rack to upper-middle position and second oven rack to lowest position, then place a rimmed baking sheet on each rack and heat oven to 400 degrees.
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2
Meanwhile, halve each zucchini lengthwise.
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3
With a small spoon, scoop out the seeds and most of the flesh so that the walls of the zucchini are about 1/4-inch thick all the way around.
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4
Season the cut sides of the zucchini with salt and pepper and brush them lightly with 2 tablespoons of the oil.
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5
Set the zucchini halves cut-side down on the hot baking sheet that has been preheating on the lower rack.
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6
Meanwhile, toss the potatoes with 1 tablespoon of the olive oil, salt, and pepper, to taste, in a small bowl and spread in a single layer on the hot baking sheet that has been preheating on the upper rack.
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7
Roast the zucchini until slightly softened and skins are slightly wrinkled, about 10 minutes while simultaneously roasting the potatoes until they are tender and lightly browned, 12 to 14 minutes.
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8
When the zucchini has finished baking, remove it from the oven and using tongs, flip the zucchini halves over on the baking sheet and set aside.
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9
While the zucchini and potatoes are roasting, heat the remaining tablespoon oil in a 12-inch skillet over medium heat until shimmering, about 2 minutes.
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10
Add the onion and cook, stirring occasionally, until softened and beginning to brown, about 10 minutes.
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11
Stir in the garlic and cook until fragrant, about 30 seconds.
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12
Add the tomatoes and cooked potatoes; cook, stirring occasionally, until heated through, about 3 minutes.
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13
Off the heat, stir in the basil, 1/2 cup cheese, and salt and pepper to taste.
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14
Divide filling evenly among the zucchini halves on the baking sheet, spooning about 1/2 cup into each, and packing it lightly; sprinkle with remaining cheese.
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15
Return the baking sheet to the oven, this time to the upper rack, and bake the zucchini until heated through and cheese is spotty brown, about 6 minutes.
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16
Serve immediately.
