3mediumred potatoes, about 1 pound, cut into 1/2-inch cubes
1mediumyellow or red onion, chopped fine
5largecloves garlic, finely minced
3mediumtomatoes, about 1 1/4 pounds, seeded and chopped
⅓cupshredded fresh basil leaves or 1 tablespoon dried
6ouncesMonterey Jack cheese, shredded (about 1 1/2 cups)
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.
Meanwhile, halve each zucchini lengthwise. 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. Season the cut sides of the zucchini with salt and pepper and brush them lightly with 2 tablespoons of the oil. Set the zucchini halves cut-side down on the hot baking sheet that has been preheating on the lower rack.
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. 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. 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.
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. Add the onion and cook, stirring occasionally, until softened and beginning to brown, about 10 minutes. Stir in the garlic and cook until fragrant, about 30 seconds. Add the tomatoes and cooked potatoes; cook, stirring occasionally, until heated through, about 3 minutes. Off the heat, stir in the basil, 1/2 cup cheese, and salt and pepper to taste.
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. 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. Serve immediately.