Cut the potato bread slices into 1 inch cubes. Place them in a large bowl or spread out onto a baking sheet and set aside to stale overnight.
Heat a large saute pan over medium heat and add the butter. Add the mushrooms and saute until soft, about 4-5 minutes.
Add the flour and stir to coat the mushrooms. Then add the broth a little bit at a time, whisking constantly. Add the diced onion and celery and stir to combine.
Add the rosemary, thyme, salt and pepper. Turn the heat to low and simmer for 20 minutes until the sauce is thick and the onion is translucent. Set aside to cool completely.
In a medium bowl add the eggs and cream and whisk them together until completely combined.
When the sauce is cool, pour it into a large bowl and add the stale bread. Gently mix the bread and sauce together until coated, then pour in the custard. Gently combine.
Preheat the oven to 350 degrees F/177 degrees C.
Pour the bread pudding into a baking dish and bake for 25-30 minutes, or until the internal temperature reaches 165 degrees F/73 degrees C.
Garnish with fresh thyme, serve warm and enjoy!