Preheat oven to 400°F. On a baking sheet, toast bread until golden brown, about 5-10 minutes. Carve off the top of the pumpkin. Scrape out seeds and any loose fibers from inside pumpkin with a spoon. Season inside of pumpkin with 1/2 tsp salt and pepper. Whisk together cream, broth, mustard, garlic, 1 tsp salt, and 1/2 tsp pepper in a bowl. Put a layer of bread in bottom of pumpkin, then cover with about 1 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, using all of cream mixture. (You may have some bread and cheese left over.) Cover pumpkin with top and put in an oiled small roasting pan. Brush outside of pumpkin all over with olive oil. Bake until pumpkin is tender and filling is puffed, 1 1/4 to 1 1/2 hours.
Make ahead factor: Pumpkin can be filled 2 hours before baking and chilled.