Add flour, salt, and yeast to the bowl of stand mixer and mix with a dough hook on low until combined. In a separate 4-cup measuring cup, add eggs and sugar and whisk together to combine. Add milk and whisk together.
With the mixer on low, add milk mixture to the dry ingredients. Mix on low until dough forms. Increase speed to medium and knead dough until it's smooth and no longer sticks to the sides, about 10 minutes. If the dough is sticking for a while, add more flour until it only sticks to the bottom.
Reduce speed to medium low. Add butter to the dough, 1 tablespoon at a time until all the butter is absorbed. Do not add the next tablespoon until you don't see the previous tablespoon anymore. Once all the butter has been added, increase the speed and knead for 6 more minutes. Once you finish kneading, shape into a ball. Lightly grease another large bowl and place the ball of dough into bowl. Cover with a kitchen towel and let it rise for 2 hours.
Prepare two baking sheets by lining with parchment paper. Once dough has risen, punch it down with your fist and remove from the bowl. Lightly dust your counter with flour and place the dough on top. Form into a disk. Cut dough into 2 even halves. Working with one half at a time, roll into a 18x12 inch rectangle, with the long side facing you. Spread 2 tablespoons of the softened butter over the rectangle. Roll the dough into a tight log that is 18 inches long, making sure the dough is even thickness. Cut the log into 6 even pieces (each piece being 3 inches long).
Grabbing one piece of dough at a time, roll into a 10 inch log. Curl the dough into a spiral and tuck under the end piece and push your finger into the top center of the bun to seal it. Repeat with 5 other pieces of dough and place on one baking sheet. Melt the final 2 tablespoons of butter and brush the buns with butter. Repeat with second half of dough. Place second batch of buns on the other baking sheet and butter them. Cover the baking sheets with the buns with plastic wrap and set aside to prove for another 1.5-2 hours.
Make the buns:
Preheat oven to 350 degrees. Make sure both oven racks are placed in the center of the oven. Once the buns have doubled in size and are puffy, place them in the over to bake for 15 minutes or until they begin to turn golden brown on the outside. Remove from oven and let them cool for 10 minutes.
Dust warm buns with powdered sugar. Serve immediately or within 24 hours.
Notes
Recipe adapted from Bread Illustrated by America's Test Kitchen