In a large mixing bowl, combine 2 cups of flour and yeast.
In a small saucepan, heat milk, sugar, butter, and salt until warm (120°F to 130°F) and butter is almost melted.
Add milk mixture to flour mixture; add egg. Beat with an electric mixer on low speed for 30 seconds, scraping bowl constantly. Then beat on high speed for 3 minutes.
Stir in as much of the remaining flour as you can. Knead in enough remaining flour to make a moderately soft dough that is smooth and elastic (3 to 5 minutes total).
Shape dough into a ball. Place in a greased bowl; turn once. Cover; let rise in a warm place until double in size (about 1 hour).
Punch dough down. Turn out onto a lightly floured surface. Cover; let rest for 10 minutes.
Roll dough into a 12x8-inch rectangle. Spread with softened butter. Combine brown sugar and cinnamon; sprinkle over buttered dough.
Roll up from a long side; seal seam. Slice into 12 pieces. Place in a greased baking dish. Cover; let rise until nearly double (about 30 minutes).
Bake in a 375°F oven for 20 to 25 minutes or until golden brown. Cool slightly.