Cut the squash in half and scoop out the seeds and pulp, then slice the halves into 1 1⁄2-inch wedges. Add butter and 1 tablespoon of the oil to a 10-by-15-inch baking sheet, and place in the oven until the butter melts, about 2 minutes.
Remove the tray from the oven, and roll the butter around so that it evenly coats the pan. Arrange the squash wedges in one layer, and sprinkle with thyme, 1⁄2 teaspoon salt, and lots of freshly ground black pepper. Roast for 15 minutes, or until deeply browned underneath. Flip the slices, and season the second side on top with another 1⁄2 teaspoon salt and more pepper. Scatter the garlic cloves in the pan, and return the pan to the oven to roast for another 12 to 15 minutes, until the wedges are browned on the second side. Don’t worry if the squash isn’t fully cooked yet. Carefully pour the broth and vinegar into the pan, and roast for another 10 to 15 minutes, until the squash is tender and the liquid is somewhat cooked off.
Use the back of a spoon to swirl plain yogurt onto a serving platter into a thin layer. Toss the arugula with the remaining tablespoon olive oil and a pinch of salt and pepper, and scatter over the yogurt. Arrange the squash wedges on top, scrape out every bit of pan juice that’s left, and pour it over the squash.
