Step 1In the bowl of a stand mixer or in a large bowl, drizzle the yeast over the warm milk, stirring to combine. Set aside for a few minutes to hydrate the yeast.
Step 2Meanwhile, in a separate large bowl, sift together the flour, sugar and salt.
Step 3Using the paddle attachment with a stand mixer, or a hand-held mixer, beat the softened butter into the yeast mixture. With the mixer running, add the flour mixture until thoroughly combined, scraping down the sides of the bowl as needed (as the dough thickens you may need to do this by hand). Continue to mix on medium speed until the dough appears sticky but becomes smooth to the touch when you roll a small piece into a ball, about 2 minutes.
Step 4Form the dough into a disc and transfer it to a lightly greased bowl. Cover loosely with plastic wrap and set aside to rise in a warm place until doubled in volume, about 1 hour (time will vary depending on the temperature in the room).
Step 1In a medium saucepan, melt the butter and brown sugar together over medium heat, stirring frequently, just until the brown sugar starts to dissolve into the butter to form a sauce, about 5 minutes. Remove from the heat.
Step 2Pour one-third of the butter-brown sugar mixture into a greased 10-inch cake pan, then sprinkle in half of the chopped walnuts in an even layer. Keep the remaining butter-sugar mixture in a warm place so it stays pourable.
Step 3In a small bowl, combine the cinnamon and sugar. Set aside.
Step 4Punch down the monkey bread dough and place it on a lightly floured surface. Divide the dough into four equal pieces, and loosely drape a piece of plastic over the dough.
Step 5Using your hands, roll one piece of the dough into a 12-inch-long log. (The dough is moist and it may not be perfectly smooth.) Cut the log crosswise into 10 equal pieces. Roll the pieces in the cinnamon-sugar mixture and place them side by side, gently touching (not tightly packed), on top of the walnuts and butter-brown sugar mixture. Continue with the three remaining pieces of dough, forming the logs, then rolling the cut pieces in cinnamon-sugar and placing them in the pan (the pieces should cover the base of the pan).
Step 6Sprinkle the remaining chopped walnuts over the top of the dough. Cover the pan loosely with plastic wrap and set aside to rise until the dough has more than doubled, about 1 hour. Meanwhile, heat the oven to 350 degrees.
Step 7Unwrap the risen dough and pour over the remaining butter-brown sugar mixture. Place the pan in the oven and bake until the monkey bread is puffed and golden brown, about 35 to 45 minutes. Cool the monkey bread, still in the pan, on a rack for 15 minutes. Invert the monkey bread onto a serving plate or platter and allow the bread to cool slightly. Serve warm.