Place the butter in a small, heavy-bottomed saucepan, and cook over medium heat, stirring constantly. First, the butter will melt, and then it will boil and foam. Continue to stir, and watch carefully. The protein solids will separate and drop to the bottom of the pan.

As soon as you begin to smell a nutty smell and begin to see a golden brown color start forming around the edges of the saucepan, remove the pan from the heat and continue to stir. Once the bubbles clear, you will be able to see whether the protein has begun to brown. If not, return to the heat briefly, stirring constantly, and remove once the butter has begun to brown.

Continue to stir, as it will continue to brown off the heat. Pour the brown butter into a small, heat-safe bowl and set it aside to cool until no longer hot to the touch.

Place the bread flour and yeast in the bowl of a stand mixer, and use a handheld whisk to combine well. Add the salt, and whisk to combine. Add the cooled browned butter, sweet potatoes, honey and milk, then attach the dough hook to the stand mixer, and mix on low speed until combined. Raise the mixer speed to medium and mix for about 5 minutes. The dough should be smooth and stretchy.

Spray a silicone spatula lightly with cooking oil spray, and scrape down the sides of the bowl. Transfer the dough to a lightly oiled bowl or proofing bucket large enough for the dough to rise to double its size, and cover with an oiled piece of plastic wrap (or the oiled top of your proofing bucket).

Set the dough in a warm, draft-free environment to allow it to rise to double its size (about 1 1/2 hours).

Once it has doubled, place it in the refrigerator for at least 15 minutes or until it is chilled. This will make it much easier to handle.

Line a rimmed baking sheet with unbleached parchment paper and set it aside.

Remove the dough from the refrigerator and turn it out onto a lightly floured surface and, using the scrape and fold kneading method and a very light touch, sprinkle the dough with more flour and knead it lightly, sprinkling with flour when necessary to prevent it from sticking, scraping the dough off the floured surface with a floured bench scraper, then folding it over on itself. Repeat scraping and folding until the dough has become smoother. Do not overwork the dough or you will incorporate too much flour and it will not rise properly.

With a floured bench scraper, divide the dough into eight pieces of equal size. Shape each piece into a round, and place the rounds on the prepared baking sheet, about 3-inches apart from one another.

Sprinkle the tops of the rounds lightly with flour. Cover the baking sheet with lightly oiled plastic wrap, and place in a warm, draft-free location until nearly doubled in size (about 1 1/2 hours).

About 25 minutes before the buns have finished rising, preheat your oven to 375°F, then remove the plastic wrap and brush the rolls generously with the egg wash.

Allow to finish rising, and then place the baking sheet in the preheated oven and bake for about 10 minutes.

Reduce the heat to 350°F, remove the buns from the oven, and brush the tops with the melted butter.

Return the baking sheet to the oven and bake until the internal temperature of the buns reaches about 185° and they are golden brown all over (about another 8 minutes).

Remove from the oven and cover with a tea towel as they cool before slicing and serving.