Butter a 9 x 13 baking dish. Add stale bread cubes; set aside.
In a large sauté pan cook sausage, onion, and garlic together until sausage is done. Top bread cubes with sausage mixture.
Sauté mushrooms in same pan until browned. Add to bread and sausage. Top with cubed squash.
In a large mixing bowl whisk together milk, cream, eggs, salt, and pepper. Fold in cheese. Pour egg mixture over bread mixture and allow bread to soak up custard mixture for 20-30 minutes, pressing bread into egg mixture a few times. Bake immediately or cover with plastic wrap and up to 2 days.
When ready to bake, preheat oven to 325, remove bread pudding from refrigeration, remove plastic wrap and allow to rest at room temperature for at least 30 minutes. Bake for 40-45 minutes or until custard is set in the middle and the mixture is puffed and golden brown.