1. In a mixing bowl, combine 2 cups of flour and yeast.
2. In a saucepan, heat milk, sugar, butter, and salt until warm (120-130°F).
3. Add milk mixture to flour mixture; add egg. Beat with an electric mixer on low speed for 30 seconds, scraping bowl. Beat on high speed for 3 minutes.
4. Stir in as much remaining flour as you can. Knead dough on a lightly floured surface until smooth and elastic (3-5 minutes).
5. Shape dough into a ball. Place in a greased bowl; cover and let rise in a warm place until doubled in size (about 1 hour).
6. Punch dough down. Turn out onto a lightly floured surface. Roll into a 12x8-inch rectangle.
7. Spread softened butter over dough. Combine brown sugar and cinnamon; sprinkle over butter.
8. Roll up dough starting from a long side. Pinch seam to seal. Cut into 12 slices.
9. Place slices in a greased baking pan. Cover and let rise until nearly doubled (about 30 minutes).
10. Bake in a 375°F oven for 25 minutes or until golden brown. Cool slightly.
11. For glaze, combine powdered sugar, milk, and vanilla. Drizzle over warm rolls.