Activate the yeast: Pour warm milk (110-115 degrees F) into the bowl of stand mixer or in a separate bowl. Add sugar and yeast. Stir, and let it stand for about 10 minutes until it foams up. If it doesn't, discard and start over with fresh yeast.
Set up the dough hook attachment in the stand mixer. To the yeast mixture, add the eggs, ¼ cup melted butter, honey, and salt. Mix over medium speed until evenly combined.
With the mixer on medium speed, gradually add flour 3 cups flour, 1 cup at a time. Add the remaining flour in ¼ cup increments as needed, mixing over medium-high speed until the dough comes together and pulls away from the bowl, about 2 minutes or so. I ended up using a little over 3 ½ cups of flour. At this point, the dough should be slightly sticky, moist, and manageable.
Transfer dough to a floured surface and knead by hand (use the lower palm of your hands) for about 3 to 4 minutes, sprinkling more flour as necessary. The dough is ready when it’s moist, slightly sticky, and manageable, and should spring back slowly when poked. Do not over-flour or over-knead.
Form into a ball and place on a lightly oiled large bowl (olive or vegetable oil are fine), making sure to coat the dough with oil as well so it doesn’t dry out. Cover bowl with plastic wrap and let it rise in a warm environment for about 1 to 2 hours, or until doubled in size. Tip: How to create a warm environment - microwave a cup of water until the microwave oven is warm, about 1-2 minutes. Turn it off. Immediately place the dough, close the door, and let it rise. You can leave the cup of water inside.
After it’s doubled in size, punch down the dough and transfer to a clean non-floured surface. Cut into 12 equal parts. Tip: I like to cut the dough in half, and then each half into 6 equal pieces.
Shape rolls: pull and stretch the outer edges of the dough into the center to form a ball, pinching at the bottom to seal the seams. Arrange on a lightly greased 9x13 in baking pan, pinched side down.
Cover the pan with plastic wrap and let it rise for another 1 hour in a warm environment, until puffed up. While the dough is rising, preheat oven to 350 degrees F.
Once the dough has puffed up, gently brush the top with some melted butter. Bake for about 15-20 minutes, or until golden brown on top.
Meanwhile, make the whipped honey butter: In a mixer, whip the softened butter with honey over medium-high speed until fluffy and combined.
Once the buns come out of the oven, brush them with some of the prepared honey butter. Let them cool slightly and serve with more of that delicious honey butter on the side. Enjoy!