In a mixing bowl, combine the warm whole milk and brown sugar. Sprinkle the instant yeast over the top and let it sit for about 5 minutes, or until it becomes frothy.
Once the yeast mixture is ready, add the melted and cooled butter, salt, and 3 1/2 cups of bread flour to the bowl. Mix until a dough forms, adding more flour if sticky.
Knead the dough for about 5-7 minutes until smooth and elastic. Place in a greased bowl, cover, and let it rise for about 1 hour or until it doubles in size.
Punch down the risen dough, divide into 8 pieces, and shape into balls. Place on a parchment-lined baking sheet and let rise for another 30 minutes.
Preheat your oven to 425°F (220°C). In a pot, bring 4 cups of water to a boil and stir in the baking soda.
Boil each bun for about 30 seconds using a slotted spoon. Remove and allow excess liquid to drain before returning to the baking sheet.
Whisk together the egg and a splash of water. Brush the mixture over the tops of each bun and sprinkle with coarse sea salt. Bake for 12-15 minutes or until golden brown.
Remove from the oven and cool on a wire rack. Brush with melted butter if desired. Serve warm or at room temperature.
