To make the dough:
In the bowl of a stand mixer, sprinkle yeast over the water.
Allow to sit for a few minutes, then whisk until smooth.
Whisk in 1/2 cup of the flour, then cover with plastic wrap and let stand in a warm spot for 30 minutes.
After the 30 minutes, add the eggs, sugar, salt, and remaining 4 cups of flour.
Fit your mixer with the dough hook and knead on medium speed until smooth, about 3-4 minutes.
Add room temp butter and continue to knead, adding a little flour to reduce stickiness if needed, until the dough is smooth, about 10 minutes.
Cover bowl with plastic wrap and let dough rise until doubled for 2 hours.
Make the filling:
Brown the butter, by adding butter to small pot over medium heat.
Stir continuously, until butter turns amber color and immediately remove from heat. This will take between 5 and 10 minutes.
Butter 9x13" baking dish.
Transfer dough to a floured surface and roll into a 15x10 inch rectangle.
Brush rectangle with half of the browned butter, leaving a 2 inch strip uncovered on one long side.
Sprinkle with cinnamon sugar.
Starting at the long side covered with sugar, roll up the rectangle snugly and pinch the seam together.
With seam facing down, cut into 10 pieces with very sharp knife.
Place pieces cut side up in prepared dish and brush with remaining brown butter.
Cover with plastic wrap and let rise in refrigerator overnight.
The next morning, remove from refrigerator and let rise again for 1 hour.
Preheat oven to 350 degrees F.
Bake in preheated oven until golden brown, about 30 minutes.
While rolls are baking, make vanilla glaze by combining confectioners' sugar, salt, melted butter, milk, and vanilla.
Spread over warm rolls and serve immediately.