In a large bowl, stir together 1 1/2 cups of the flour and the yeast; set aside. In a small saucepan, heat and stir 3/4 cup milk, granulated sugar, 1/3 cup butter, and salt just until warm (120 degrees F to 130 degrees F) and butter almost melts. Add to flour mixture along with eggs. Beat with an electric mixer on low to medium speed for 30 seconds, scraping sides of bowl constantly. Beat on high speed for 3 minutes. Using a wooden spoon, stir in as much of the remaining flour as you can.
Turn dough out onto a floured surface. 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 lightly greased bowl, turning once to grease surface; cover. Let rise in a warm place until double in size (about 2 hours).
Punch dough down. Turn out onto a lightly floured surface; cover and let rest 10 minutes. Line 2 large baking sheets with parchment paper or nonstick foil; set aside. Roll dough in to a 20x16-inch rectangle.
In a small saucepan, melt remaining 1/4 cup butter over low heat. Add brown sugar and 1 teaspoon cinnamon; mix well. Cool slightly and spread mixture evenly over dough. Cut dough crosswise into twenty 1-inch strips. Fold each strip in half, end to end, and twist several times. Arrange twists 2 inches apart on prepared baking sheets. Cover and let rise in a warm place until nearly double in size (45 to 60 minutes).
Preheat oven to 375 degrees F. Bake for 12 to 15 minutes or until golden brown. Cool slightly on a wire rack.
In a small bowl, combine powdered sugar, vanilla, 1/8 teaspoon cinnamon and enough milk (2 to 3 tablespoons) to make drizzling consistency. Whisk until smooth and drizzle over rolls when warm.