Heat a lightly greased large sauté pan or skillet with high sides over medium heat. Add chorizo and sauté until it begins to render some of its fat, about five minutes.
Add leeks and mushrooms. Saute for an additional five minutes or until leeks become tender and chorizo is completely cooked.
Add garlic and sauté for an additional 30 seconds.
Add the rice to the pan. Stir rice until completely coated.
Add one cup of the chicken broth and scrape up any browned bits that have stuck to the bottom of the pan.
Reduce heat to medium. Stir in the pumpkin puree. Bring mixture to a simmer and continue to cook, stirring frequently, until all liquid is absorbed. Add the second cup of chicken broth and continue cooking as above. Add the white wine and thyme and again, continue cooking as above. Total cooking time will be around 30-45 minutes and by now, rice should be creamy and tender.
Remove the pan from the heat. Add the Parmesan cheese. Season with salt and pepper as desired.