Melt the butter in the microwave on 20 second intervals. Set side to cool slightly.
In a large mixing bowl or in the bowl of a stand mixer, whisk the all purpose flour, bread flour, instant yeast, brown sugar, and salt.
Add the warm water and melted butter to the flour mixture and mix until it forms a shaggy dough.
On a lightly floured surface, knead the dough by hand for 8 minutes, or in a stand mixer with a dough hook for about 5 minutes, until it forms a smooth, elastic dough.
Shape the dough into a ball, place it back in the mixing bowl, and cover with a kitchen towel. Let it rise in a warm, draft-free spot until the dough doubles in size, after about 2 hours.
Preheat the oven to 425°F. Line a baking sheet with a silicone baking mat or with parchment paper sprayed generously with cooking spray. (If you just bake your pretzel buns on parchment paper, they’ll stick to the paper.)
Prepare the baking soda bath: Bring a pot of water and baking soda to a boil.
On a clean work surface, divide the dough in 8 equal-sized pieces and gently shape them into balls, tucking the seams underneath.
Gently lower the first two to three dough balls into the boiling baking soda bath. Use a slotted spoon or two spoons to lower the dough into the pot to avoid splashing hot water.After 30 seconds, use a spoon to turn the dough balls over and boil for another 30 seconds.Use a slotted spoon to remove the dough balls from the pot and place them on your lined baking sheet. Repeat with the remaining dough balls, two at a time. While the buns are still wet, immediately sprinkle the pretzel salt or coarse salt on top. Score the tops with a small X about ¼ inch deep.
Bake for 15 to 18 minutes, until the buns are a dark brown color. Allow them to cool on a cooling rack for a few minutes, then enjoy!