In the bowl of a stand mixer, combine warm milk, brown sugar and yeast. Let sit for 5 minutes until yeast proofs (gets all bubbly).
Add 2 cups of flour into the bowl on top of the proofed yeast mixture. Stir on low using the dough hook. Once the flour has mostly incorporated, stir in melted butter and salt.
With stand mixer on, continue adding in flour, bit by bit, until dough is tacky but won't stick to your hands and the bowl is mostly clean (about 5-7 minutes). I used exactly 3 1/2 cups, but your dough could take less or more flour. The dough is ready when you press it gently with your finger and it springs back.
Remove dough and place in a clean well oiled bowl and cover with a tea towel or plastic wrap. Place in a warm area of the house and allow to rise for at least one hour. Your oven with just the oven light on is a perfect spot!
Prepare a large baking sheet with parchment paper sprayed with cooking spray or oil. Set aside.
After the dough has doubled in size, punch it down and kneed for a minute or two. Using a bench scraper or sharp knife, divide into 8 equal pieces.
Shape each piece into round buns and place on prepared baking sheet.
Second rise: Cover with a tea towel or plastic wrap. Place in a warm area of the house and allow to rise for another 30-60 minutes until doubled in size.
Meanwhile, place the water and baking soda in a medium pot over high heat. Stir to combine well and bring to a gentle boil.
Preheat oven to 400° F.
Once buns have doubled in size, dip both sides into the gently boiling baking soda water bath, no longer than 5 seconds per side.
Remove with a large slotted spoon or spider, allowing excess water to drip off before placing back on baking sheet.
Using a razor blade or small knife, slice an X on top of each bun.
In a small bowl whisk egg and splash of water together to create an egg wash. Brush tops with egg wash and sprinkle with coarse salt.
Bake at 400° F for 10-13 minutes or until deep golden brown and cooked through.
Optional: Brush with melted butter after removing from oven
Let buns cool slightly on a wire rack. Serve warm or store in an airtight container once cooled. If using as sandwiches, slice in half and serve with desired toppings.