Activate the Yeast: Combine the barely lukewarm water, brown sugar, and active dry yeast. Let the mixture stand for about 5 minutes, until bubbly. If it does not become bubbly, the water may have been too hot or the yeast may no longer be active, so repeat this step with fresh yeast and properly warmed water.
Make the Dough: Sift the all-purpose flour and sea salt together. Add the room-temperature butter and the bubbly yeast mixture.
Knead the Dough: Using a stand mixer fitted with a dough hook, knead the dough on a low setting for 8 to 10 minutes.
Rest and Divide the Dough: Cover the dough with wax paper or a clean linen towel and let it rest for 5 minutes to help prevent a skin from forming. Divide the dough into eight 100-gram (3.5-ounce) portions. If you do not have a kitchen scale, shape the dough into a long log of even thickness and divide it into 8 equal pieces.
Shape the Buns: Shape each portion of dough into a small, smooth ball.
Let the Buns Rise: Place the shaped buns on sheets of wax paper or silicone baking mats. Cover with a clean linen towel and allow them to rest and develop for about 60 minutes.
Prepare the Lye Solution: In a well-ventilated area, carefully add the premeasured dry food-grade lye to the cold water—never add the water to the lye. Step away briefly for about 10 to 15 seconds to allow any potential fumes to dissipate, then carefully whisk until the solution is clear.
Dip the Buns: Using a steel skimmer or two large spoons, carefully dip each risen bun into the lye solution for 5 to 10 seconds. Transfer the buns with the skimmer to a baking sheet lined with parchment paper or a silicone baking mat.
Score and Salt the Buns: Using a small, sharp knife, cut an X into the top of each bun to allow it to rise during baking. Sprinkle the tops with pretzel salt.
Bake the Pretzel Buns: Bake at 355°F (180°C) using the convection/Umluft setting for about 12 minutes, or until golden brown. Rotate the buns after about 6 minutes for more even baking.
Cool and Serve: Allow the pretzel buns to cool for a few minutes before serving. Enjoy them on their own, with butter, or as part of sandwiches, burgers, or other savory meals.