- Heat the oil in a large, heavy-bottomed pot over high heat. Add the onions and cook, stirring with a wooden spoon, until soft, about 5 minutes. Add the rice and stir for another minute. Add the rosemary sprig, cover with 2 cups Chicken Stock, and bring to a boil. Reduce the heat to medium low, cover the pot, and simmer for about 5 minutes. Add another cup or two of Chicken Stock and the pumpkin. Stir well, then cover and simmer for 10 minutes.
- Season the shrimp with salt and pepper and add to the pot along with the mushrooms and the remaining Chicken Stock. Raise the heat to medium and cook about 5 minutes, stirring occasionally. Test the rice for doneness: It should be soft, with a slight bite in the center. Remove the sprig of rosemary and fold in the Parmesan, butter, and chives. Season with salt and pepper and scatter thyme leaves on top. Serve immediately.
Basic Chicken Stock
- Combine the chicken carcasses, onions, carrots, celery, garlic, thyme, bay leaf, and peppercorns in a large heavy-bottomed pot. Cover with 12 cups cold water and bring to a boil. With a spoon, skim and discard the foam that rises to the top. Reduce the heat to medium low and simmer until reduced by about half, about 3 hours. Strain the stock through a fine-mesh strainer over a large bowl. The stock is ready to use, or chill and freeze for future soups and stews