Preheat oven to 350˚F.
Pour milk and half of sugar into a mixing bowl and stir together.
Sprinkle yeast over milk and sugar and allow mixture to sit for 4 to 5 minutes (yeast should begin to bubble and foam).
Stir in remaining sugar, salt, butter, and eggs. Begin adding flour, ½ cup at a time, stirring to incorporate after each addition.
Once all the flour has been added, dump mixture onto a clean and lightly floured surface and knead dough for 5 to 7 minute or until smooth and elastic, adding more flour, 1 teaspoon at a time as needed.
Once smooth dough has formed, place dough into a lightly greasy bowl, cover with a clean, damp towel and place in a warm area until dough has doubled in size. About 1 hour and 20 minutes.
Place both butters for filling and the glaze into a medium saucepan and simmer for 15 to 20 minutes or until butter begins to toast, brown and produce a nutty smell.
Divide the butter into two separate bowls and allow them each to cool, about 20 minutes. In another small bowl whisk together the superfine sugar and cinnamon.
Once dough has doubled in size, punch down the center and turn onto a clean and lightly floured surface. Roll dough out into a 12”x 19” rectangle and about ¼″ thick. Generously brush the entire surface of the dough with one of the bowls of browned butter. Sprinkle evenly with cinnamon-sugar mixture. Tightly and evenly roll rectangle from one end to the other and gently pinch the seam shut. Place cinnamon roll log seam side down and cut into 10 even cinnamon rolls.
Place cinnamon rolls into a lightly greased baking dish and cover with a clean, damp towel.
Store in a warm place until cinnamon rolls double in size about 1 hour.
Uncover and bake for 25 to 30 minutes or until golden brown.
Remove from oven and cool for 10 minutes.
For the glaze: Stir milk, vanilla and cinnamon into the butter until fully incorporated. Stir sugar into the butter mixture, ¼ cup at a time until fully incorporated and mixture is smooth.
Pour ½ of the glaze over the slightly cooled cinnamon buns and allow cinnamon buns to continue to cool, about 30 minutes. Drizzle remaining glaze over cinnamon buns and serve.