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1. Melt butter and keep cooking it over medium heat for a few additional minutes to brown. Remove from heat and set aside to cool slightly.
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2. Combine your warmed milk and yeast in a small bowl and set aside for 5-7 minutes, or until foamy.
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3. In the bottom of the bowl of an electric mixer combine flour, sugars, salt and spices. Add just 1/4 cup of your browned butter and stir to combine. Add yeast-milk mixture, pumpkin and egg and mix combined. Switch mixer to a dough hook and run it for 5 minutes on low.
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4. Scrape mixture into a large oiled bowl and cover with plastic wrap. Set aside for 1 hour in a draft-free place; it should just about double.
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5. While it is rising, line the bottom of a large 9 x 13 metal pan with parchment paper and butter the sides of the pan and the paper.
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6. Once risen, scoop dough onto a very well floured surface and flour the top of it well. With a rolling pin, roll the dough to an approximately 16x11-inch rectangle. Brush reserved browned butter over dough.
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7. Stir together filling ingredients and sprinkle mixture evenly over dough. Starting on a longer side, roll the dough into a tight spiral. With a sharp serrated knife, using absolutely no pressure whatsoever, gently saw your log into approximately 1-inch sections.
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8. Place buns into prepared pans. You can sprinkle any sugar that fell off onto the counter over them. Cover pan with plastic wrap and let rise for another 45 minutes. If you're doing this ahead of time, you can now put them in the fridge overnight. In the morning, leave them out for an hour to warm up and finish rising.
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9. Pre-heat the oven to 350u00b0F. Meanwhile, you can make the glaze. Whisk all the ingredients together until a drippable/spreadable glaze forms (add more milk if needed).
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10. Remove the plastic wrap from the pan, and bake the buns for 20-25 minutes, until golden brown. Drizzle with glaze and serve.
