Preheat oven to 325. Grease a 3 quart glass baking pan.
Heat a large skillet over medium heat. Add 6 tablespoons butter. When melted, add the celery and shallots. Reduce heat to medium low and cook for 30 minutes, stirring occasionally.
Add bread and cook 10 more minutes, letting the bread soak up the butter. Remove from heat.
Add potatoes to a separate pot, cover with water, bring to a boil, then simmer for 8 minutes or until soft and mashable. Drain, return to pot, and mash them. Add the egg, milk, butter, and salt, stirring gently until combined. Then mix in the bread mixture and the fresh parsley.
Add all of this to the baking pan and bake for 35-40 minutes until the edges are nicely browned.