Preheat the oven to 375 degrees F.

Cut the lid off the pumpkin and scoop out the seeds and fibers. Scrape away some of the flesh, especially around the top, to form a large, smooth inner cavity. Make sure to leave the shell at least 1-inch thick all around. Oil the pumpkin inside and out and season inside with salt and pepper. Replace the lid. Place on a baking sheet and bake until about 2/3's cooked but still firm enough to stand and act as the soup container, about 40 minutes. Do not over-bake. If a good deal of liquid gathers in the bottom, spoon out and discard. Set aside; it will stay warm on its own a good while.

Bring the stock to a low simmer in a saucepan. Heat the remaining 2 tablespoons olive oil in a large saute pan over medium-high heat until hot. Add the onion and cook until soft but not brown, 2 to 3 minutes. Add the thyme, stir, and add 2 cups of the stock. Bring to a boil. Add the pastina, stir well, and reduce the heat to maintain a slow simmer. Season with salt and pepper. Simmer, adding the stock 1/2 cup at a time as the previous addition is absorbed and stirring occasionally to prevent the pastina from sticking to the bottom of the pan, until the pasta is al dente, about 15 minutes. Add the roasted squash and turkey to reheat. Stir well. The consistency should be quite loose, like a thick soup. Add more stock, if necessary. Add the 1/2 cup cheese and let melt for a moment before stirring in. Taste, for seasoning.

Ladle the pastina into the reserved pumpkin shell and garnish with the remaining 2 tablespoons Parmesan. Replace the lid and take to the table immediately.

Variation with Greens: For a colorful and nutritious addition, cut several handfuls of winter greens such as spinach or chard into a chiffonade and stir into the pastina just to wilt before serving.