Grease a 9x9x2-inch baking pan; set aside. In a large bowl, combine 1 cup of the flour and the yeast; set aside.
In a small saucepan, heat and stir milk, granulated sugar, 1/2 cup butter, and salt just until warm (120 degrees F to 130 degrees F) and butter almost melts. Add milk mixture and eggs to flour mixture. Beat with an electric mixer on low to medium speed for 30 seconds, scraping sides of bowl constantly. Beat on high speed for 2 minutes or until smooth. Beat in as much of the remaining flour as you can with the mixer. Stir in any remaining flour to make a stiff batter.
Spoon half of the batter into the prepared baking pan. In a small bowl, stir together brown sugar, 1/4 cup butter, and cinnamon. Stir in walnuts. Spoon nut mixture over the batter in the pan. Drop remaining batter by spoonfuls over nut mixture. Cover and let rise in a warm place until double in size (about 1 hour).
Preheat oven to 350 degrees F. Bake for 30 minutes or until golden brown. Cool on a wire rack 30 minutes before serving, or cool completely before serving. Spread with Cream Cheese Icing.
Cream Cheese Icing
In a small bowl, combine one 3-ounce package softened cream cheese with 2 tablespoons softened butter and 1 teaspoon vanilla. Beat with an electric mixer until combined. Gradually beat in 2-1/2 cups powdered sugar until smooth. Beat in enough milk, 1 teaspoon at a time, to reach spreading consistency. Makes 1-1/4 cups.