The Delicata is a moist, slightly sweet squash similar in texture to the butternut, with pale yellow skin and dark green stripes. They tend to be small, which makes them perfect for a single serving. In this recipe, roasting brings out the sweetness of the flesh, and a flavorful stuffing of spinach, mushrooms, and tomato adds interest and color.
Position a rack in the middle of the oven and preheat to 400 degrees F.
Cut the squash in half in lengthwise through the stem end. Scoop out the seeds and discard. Cut a thin slice from the bottom of each squash half so they will sit flat.
Place the squash halves, cut side up, on a rimmed baking sheet. Roast the squash until it is crisp-tender but not soft, about 10 to 15 minutes. Let cool.
From just 4 of the halves, carefully remove some of the flesh, leaving enough on the skin to form a rigid shell (at least 1/4 inch thick). Don't be tempted to remove too much of the flesh, or the shell will collapse or tear when you stuff it. Then remove all of the squash from the remaining 2 halves, discarding the shells. Dice the scooped-out flesh into 1/2-inch pieces and set aside. Place the 4 shells back on the baking sheet.
Meanwhile, in a large skillet, heat half of the olive oil over medium-high heat until hot. Add the sliced mushrooms and cook for 3 to 4 minutes, then stir and continue cooking until the mushrooms are tender, 5 to 10 minutes. Season to taste with salt and pepper, and then stir in the thyme leaves. Transfer the mixture to a bowl and set aside at room temperature.
Bring the oven to 375 degrees F.
Add the remaining oil to the skillet and heat over medium heat until hot. Add the onions and the red pepper flakes, and cook, stirring frequently, until the onion is soft, 5 to 8 minutes. Add the garlic and cook, stirring constantly, until the garlic is fragrant, about 2 minutes. Add the spinach and stir until just wilted, about 1 minute. Stir in the tomatoes, mushrooms, and diced squash, and cook until the mixture is hot, about 2 minutes. Season to taste with salt and pepper.
Divide the hot filling among the 4 squash halves and sprinkle with the grated cheese. Bake until the stuffing is hot and bubbling, 15 to 25 minutes. Serve hot.