1. In a large mixing bowl, combine 2 cups of flour and yeast.
2. In a saucepan, heat milk, butter, sugar, and salt until warm (120-130°F).
3. Add milk mixture to flour mixture; add eggs. Beat with an electric mixer on low speed for 30 seconds, scraping bowl constantly. Beat on high speed for 3 minutes.
4. Stir in as much of the remaining flour as you can. Knead dough on a lightly floured surface until smooth and elastic (6 to 8 minutes).
5. Shape dough into a ball. Place in a greased bowl; turn once. 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. Divide in half. Cover and let rest for 10 minutes.
7. Roll each half of dough into a 12x8-inch rectangle. Spread with softened butter. Combine brown sugar and cinnamon; sprinkle over butter.
8. Roll up each rectangle, starting from a long side. Seal seams. Slice each roll into 12 pieces. Place slices in greased baking dishes.
9. Cover and let rise until nearly doubled (about 30 minutes).
10. Bake in a 375°F oven for 20 to 25 minutes or until golden brown.
11. For icing, combine powdered sugar, milk, and vanilla. Drizzle over warm rolls.