Microwave milk and butter until almost melted. Whisk in sugar and salt. Set aside.
Using a mixer and dough hook, combine 2 1/2 cups of flour and yeast on low. Slowly add milk mixture, then eggs, one at a time, follow by vanilla. Add more flour, 1/2 cup at a time. Mix until the dough clears the sides of the bowl, about 2 minutes. Continue 2 more minutes or until you can knead by hand.
Shaping dough into a ball, place in a oiled bowl, turing it over to oil the top. Cover the bowl with plastic wrap. Let the dough rise for 1 hour.
Roll dough into a 20-by-16-inch rectangle on a floured surface. Spread softened butter over the surface of the dough. In a small dish, mix cinnamon and sugar and sprinkle on top of the butter.
Roll dough into tube. Cut the tube into 12 pieces and place each piece spiral side up in a 9-by-13-inch baking dish coated with non-stick cooking spray. Cover and let the rolls rise for 1 hour.
Preheat the over to 350 degrees. Bake the rolls for 15-20 minutes or until golden brown. Whisk together glaze ingredients, using just enough milk for the desired consistency. Spread glaze over the top while the rolls are still warm.