Place baguette slices on a large baking tray and toast for 5-7 minutes, until slightly crispy. Remove from oven and allow to cool slightly.
Cut a large circle around the stem of the pumpkin(s) to create a lid. Remove pumpkin seeds and innards. Season inside of pumpkin with 1/2 tsp salt.
In a medium bowl, whisk together cream, milk, chicken/vegetable broth, nutmeg, thyme, salt, and black pepper. In a separate bowl, combine grated cheeses.
Place a layer of toasted bread in bottom of pumpkins, then cover with about 3/4 cup cheese and about 1/2 cup cream mixture. Continue layering bread, cheese, and cream mixture until pumpkin is filled to about 1/2 inch from top. If you have any cream mixture left over, pour it on top.
Place top back on pumpkins and brush the entire outside of the pumpkins with olive oil. Bake for an hour and a half, until the pumpkins are slightly soft to the top and filling puffs up slightly.
To serve, cut pumpkins in half or quarters and top with more fresh thyme!