1. Heat the milk in a small saucepan until it starts to bubble, then remove from heat. Mix in butter and stir until the butter melts. Allow to cool slightly until lukewarm.
2. In a large mixing bowl, combine 2 1/4 cup flour, yeast, sugar and salt and whisk to combine. Add water, egg and the milk mixture. Beat well with an electric mixer or using a wooden spoon. Add the remaining flour, 1/2 cup at a time, using a wooden spoon to stir well after each addition (dough will be too thick and sticky to use the mixers at this point).
3. When the dough has just pulled together, turn it out onto a lightly floured surface and knead until smooth, about 5 minutes. (dough will spring back when lightly pressed and will loose some stickiness)
Cover the dough with a damp cloth and let rest for 10 minutes.
4. Meanwhile, brown your butter by melting it in a small saucepan. Butter will melt, then foam, then turn clear golden, then start to turn brown and smell nutty. Keep your eyes on the saucepan and remove from heat when brown bits begin to form and the butter smells nutty. While butter cools slightly, mix together brown sugar and cinnamon in a small bowl.
5. On a lightly floured surface, roll out dough into a 12x9 inch rectangle. (use your 9x13 baking dish as a guide.) Using a pastry brush- slather the dough with most of the brown butter. (It will feel like a lot, but use most of it. I used about 3/4 of it.)
6. Sprinkle dough with cinnamon sugar mixture and press in lightly. Roll up dough tightly and pinch seam to seal. Cut into 12 equal size rolls and place in a 9x13 baking dish.
7. Drizzle with remaining brown butter. Cover and let the rolls rise in a warm place until doubled, about 30 minutes. (I let mine rise in an OFF oven) **
8. Preheat oven to 375 degrees F. Bake in the preheated oven for 20 minutes, or until browned. Let cool for about 10 minutes and then drizzle with icing. (directions below) Serve warm.
Place powdered sugar and malted milk powder in a medium bowl and whisk to combine. Begin drizzling in milk and whisking. Use as much or little milk as you need to reach your desired consistency. Add vanilla and whisk.
**Note: I prepared my dough at night and baked the next morning. If you chose to do this, complete steps 1-7 and then cover the pan with plastic wrap and refrigerate. When you're ready to bake, allow rolls to come to room temperature for about 20 minutes before baking.
Recipe barely adapted from Baker Chick.