Scald 1 cup milk (heat to steaming). In a mixing bowl combine warm milk, yeast and sugar. Let yeast start to bubble, about 5 minutes.
Add 12 tbsp butter and eggs to mixer and beat, with the paddle attachment, until slightly blended. Stir in flour and salt, about 2 minutes. Scrape down sides of bowl and continue mixing on medium speed to develop the dough, 3 minutes more.
Transfer dough to a greased bowl and cover with plastic wrap; set aside in a warm place and let rise until doubled, about 1 hour. Grease 2 large-cup muffin tins. Melt 6 tbsp butter and stir i 1 1/2 tsp maple extract; set aside.
Gently punch down dough and divide in half. Roll into 2 12x18 inch rectangles on a lightly floured work surface. Spread maple-butter mixture evenly over both rectangles. Sprinkle each with half the brown sugar and walnuts. Roll tightly into logs, starting at the long edge, and pinch seams together. Cut each log into 6 3-inch pieces for a total of 12 buns. Place in muffin tins cut side up, cover and allow to rise for 30 minutes. Heat oven to 325°F. Bake until golden brown, 28 to 30 minutes.
Combine caramel topping and 1 1/2 tsp maple extract. Carefully remove hot buns from pan and place on a clean baking sheet;drizzle with caramel.
For icing: Melt 3 tbsp butter and stir together with confectioners' sugar and 2 tbsp milk; drizzle over buns. Serve warm or cool. Store airtight for up to two days.