Heat 2 tablespoons of the butter in a small saucepan in medium heat until it turns to light brown and you see small brown bits at the bottom of the pan, 2-3 minutes. Pour in the milk and let it come to 110-F degrees. (Note: This happens very quickly.)
Place the butter and milk mixture in a medium-size mixing bowl. Stir in the yeast and 1/4 cup of the sugar. Let it sit for 10 minutes or until it foams.
Stir in the pumpkin puree and salt. Fold in the flour in 3 additions.
Transfer the dough onto a well-floured surface and knead for 10 minutes. It should be an elastic and slightly sticky dough.
Use the olive oil to grease a large bowl. Place the dough into the bowl seam side down and roll it inside the bowl to ensure that it is covered with the olive oil. Cover it with stretch film and let it sit on the kitchen counter (or in a warm part of your house) until it doubles in size, about 1 1/2 hour.
In the mean time, mix the remaining butter, cinnamon, nutmeg and 1 cup sugar in a small bowl. Fold in the walnuts. Set aside.
Preheat the oven to 350 F Degrees.
Transfer the dough onto your kitchen counter and roll it out to a 12X9 inch rectangular. Sprinkle it with the butter, sugar, walnut, and cinnamon mixture.
Cut the dough lengthwise into 6 equal pieces. Then stack them on top of each other. Cut the strip into 6 equal pieces.
Place them into a 9X5-inch loaf pan. (* See the pictures in the blog post for visual instructions.)
Cover it lightly with stretch film and let it rise (in a warmer part of your house) for 30 minutes.
Bake for 35 minutes, or until the top part of the bread turns golden brown.
Allow the bread to cool on a wire rack for 30 minutes before slicing.