Adjust the oven rack to its lowest position and preheat it to 350°.
Heat the oil in a large skillet over medium-high heat. Remove the sausage from its casing and cook it in a large pan, breaking it up until done. Remove the sausage to a large plate.
In the same pan, sautee the onions over medium-low heat until translucent. Add the minced garlic and cook for 1-2 minutes.
While the sausage is cooking, wash, dry, and carve the pumpkin. Cut the top of the pumpkin off and scoop out the insides, leaving the flesh of the pumpkin wall intact.
Salt and pepper the inside of the pumpkin.
In a large bowl, mix the sausage, onion, garlic, cubed bread, cheese and thyme.
Add the nutmeg, egg, and Dijon mustard to the cream in a measuring cup and whisk until everything is incorporated.
Add the cream to the bread mixture and combine. The bread should be moist. Add more cream if needed.
Salt and pepper the stuffing to taste.
Stuff the pumpkin with the bread all the way to the top.
Dot the top of the stuffing with butter.
Put the pumpkin on a foil-lined baking sheet. Put a foil collar around the base of the pumpkin. Put the top on the pumpkin. If the pumpkin will not fit in your oven put the cap next to the pumpkin and cover the pumpkin with foil.
Bake for about 90 minutes, depending on the size. Take the top or foil off the pumpkin 30 minutes before it is done.
When the pumpkin is done, put the pumpkin on a large plate or platter.
To serve, scoop out the stuffing with the flesh of the pumpkin. Or, cut the pumpkin into slices.