Divide the enriched sweet dough into two portions. Form the two portions into loose dough balls, cover, and allow to rest for ten minutes.
While dough is resting, mix chopped walnuts, brown sugar, cinnamon, and salt together.
Roll one dough ball out into a 14" x 14" (35 cm x 35 cm) square. See video above in post for a time-lapse of how to form the wreath.
Spread 2 T of softened butter over the rolled dough, avoiding the top 1" (2cm) but to buttering to three other edges.
Sprinkle the cinnamon/walnut mixture evenly over the butter. Gently press it down.
Moisten the unbuttered top edge with water.
Roll up the dough, pulling and tightening it until you finish at the moistened edge.
Pinch the seam closed.
Turn the roll over so the seam is underneath.
Curve the ends of the seam around until they meet and form a circle.
Place one end inside the other and pinch the seams together, moistening slightly with water to ensure a good seal.
Place the circle onto a piece of parchment paper and on to a baking tray.
Using a bench scraper or knife, cut the roll 3/4 of the way through at the 12, 3, 6, and 9 position.
Then cut each section twice more. Be very careful not to cut the roll in half.
Pull each cut section slightly outwards, then turn it on it's side to expose the cinnamon roll center. Turn all subsequent sections the same way.
Cover with plastic wrap and set aside to proof.
Repeat with second dough piece.
Preheat oven to 350°F (175°C).
When wreaths have finished proofing (doubled in size and should be quite puffy), give them an egg wash and place in preheated oven.
Bake wreaths for 25-30 minutes until golden brown and the cinnamon center is bubbly/melted.
Remove dough wreath immediately to a cooling rack so the melted cinnamon sugar does not stick to the tray.
Mix the icing sugar, milk and vanilla (if using) until smooth.
When the wreath has cooled (20-30 minutes), drizzle with the topping.
Serve.
Store leftover wreath tightly wrapped in the refrigerator. Warm in a microwave for 30 seconds before serving.