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 and butter is almost melted.
3. Add milk mixture to flour mixture; add eggs. Beat with an electric mixer on low speed for 30 seconds, scraping bowl. Beat on high speed for 3 minutes. Stir in as much remaining flour as you can.
4. Turn dough out onto a lightly floured surface. Knead in enough remaining flour to make a moderately soft dough that is smooth and elastic (3 to 5 minutes). Shape into a ball. Place in a greased bowl; turn once. Cover; let rise in a warm place until double in size (about 1 hour).
5. Punch dough down. Turn out onto a lightly floured surface. Divide in half. Cover; let rest for 10 minutes. Roll each half into a 12x8-inch rectangle.
6. Spread each rectangle with softened butter. Combine brown sugar and cinnamon; sprinkle over butter. Roll up each rectangle, starting from a long side. Seal seams. Slice each roll into 12 pieces. Place in greased baking pans. Cover; let rise until nearly double in size (about 30 minutes).
7. Bake in a 375°F oven for 20 to 25 minutes or until golden brown. Cool slightly.
8. For icing, in a small bowl combine powdered sugar, milk, and vanilla. Drizzle over warm rolls.
Notes:
These cinnamon rolls are best enjoyed fresh but can be stored in an airtight container for up to 2 days.