Pre heat oven to 400 F. With a large knife or chainsaw (just kidding) cut the top of the pumpkin and remove all the seeds and other mush.. Then cut pumpkin into 3 to 4 inch wide segments. Remove skin of pumpkin with a potato peeler or peering knife. Cut into the pumpkin with a 2.5 inch dough cutter to make cylinders. Cut cylinders into ¼ inch slices.
Place some aluminum foil out on a cookie sheet and spread butter on sheet. Place pumpkin slices on the sheet and drizzle with olive oil, sprinkle with salt, pepper and fresh thyme. Cover sheet with another piece of foil and bake in the oven for 20 minutes or until softened. Remove from the oven and set aside to cool for a few minutes. Slice your mozzarella into ¼ wide pieces and place in between two slices of pumpkin. Crown with some grated parmigiano reggiano and place back in the oven for another 10 minutes. Remove and place on a plate, garnish with fresh thyme.

*Note: The mozzarella should be not as large as the pumpkin slices to avoid excess cheese run off when cooked.