Preheat oven to 350°F.
Add bacon to medium sauté pan and cook until crisp but still slightly chewy.
Remove bacon to paper towel-lined plate but retain bacon grease in pan. In the same skillet, add onion and celery, cook 5 minutes until softened.
Slice spiral tops off rolls and set aside. Dice bottom portion of cinnamon rolls and place in large bowl. Add bacon, onion and celery to diced rolls.
In medium bowl, combine egg, chicken stock, and thyme. Reserve 2 tablespoons stock mixture. Pour remaining stock into the bowl with the diced cinnamon rolls and mix well.
Pour the bread mixture into 8x6 baking dish. Top with reserved spiraled cinnamon bun tops. Brush the reserved chicken stock mixture onto spiral roll tops. Bake 40 minutes.
Put the milk into a small bowl and slowly whisk in powdered sugar until it forms glaze of desired thickness.
Brush glaze over top of stuffing as soon as it comes out of oven. serve warm.