Heat oven to 375°F.
Make a lid from the top of the pumpkin by cutting around the stem at a 45-degree angle. Make sure the opening is large enough to work within. Remove the seeds and fibers with a metal spoon or ice cream scoop. Reserve the seeds for another application, like pumpkin seed brittle. Brush the exterior of the pumpkin and lid with oil. Oil a round casserole dish large enough to hold the pumpkin and put the pumpkin inside.
Combine the butter, onion, salt, garlic, apple, broth, and cream in the hollow pumpkin. Replace the lid of the pumpkin to cover. Bake for 1 1/2 hours.
Remove the lid. Carefully stir in the cheese and thyme, and bake for an additional 30 minutes, uncovered. Remove the pumpkin from the oven and use a large metal spoon to gently scrape some of the inner flesh off the walls and into the soup. Puree with an immersion blender to desired consistency, being careful to avoid the sides and bottom of the pumpkin. Serve immediately...that's right, inside the pumpkin.