For the dough:
- 3/4 cup lukewarm water, divided
- 1 1/2 packets active dry yeast
- 1/2 cup lukewarm milk
- 2 tablespoons unsalted butter, melted
- 1/2 cup gently packed light brown sugar
- 3/4 teaspoon fine sea salt
- 3 cups bread flour, plus more if needed
For the boiling liquid:
- 6 cups water
- 1/2 cup baking soda
For the toppings:
- Grated cheddar cheese
- Caraway seeds
- Pretzel salt
- Dried onion flakes
- Sesame seeds
In the bowl of a stand mixer or a large mixing bowl, mix 1/2 cup of the warm water with the yeast and just a tiny pinch of brown sugar. Let the mixture sit until the yeast bubbles up, 6 to 8 minutes.
Add the remaining 1/4 cup of water, milk, butter, brown sugar, and salt and use a dough hook (or by hand) to combine. Slowly add the flour on low speed. Increase speed to medium-high (or knead by hand vigorously) until the dough is smooth and no longer sticky, adding more flour if needed, one tablespoon at a time. This should take about 6-8 minutes with a stand mixer and 12-15 minutes if kneading by hand.
Form the dough into a large ball, cover with a towel, and let the dough rest for 15 minutes. Cut the dough into 8 equal pieces. To make a hot dog bun, shape a piece of dough into a 5-inch log of approximately 1.5 inches in diameter with tapered ends. Arrange the dough logs onto a baking sheet lined with a silicone baking mat, leaving about 3 inches of space around each log. To make a hamburger bun, shape a piece of dough into a ball, 3 inches in diameter, flatten it slightly with your palm. Arrange each dough ball onto a baking sheet lined with a silicone baking mat, leaving about 3 inches around each ball. Cover the dough balls or logs with a towel. Let them rise for 30 minutes.
Once the dough has risen, preheat the oven to 400°F. Put the water in a pot and bring it to a gentle boil. Slowly add the baking soda to the water. Gently lift up each piece of dough and slowly plunge into the simmering liquid. Boil one or two pieces of dough at a time, 20 seconds per side. With a large slotted spoon, scoop the dough balls from the boiling liquid, shake off excess water, and gently place them on the same baking sheets fitted with silicone baking mats, leaving about 3 inches of space between them. With a sharp knife or a dough slasher, make a cross on the top of each hamburger bun and 3 to 4 diagonal cuts on each hot dog bun. Each slash should be about 1/4-inch deep. Sprinkle the top of the unbaked pretzel buns with desired topping(s).
Bake for about 20 minutes, or until the pretzel buns develop dark caramel color on the outsides. Remove the buns from the oven and let them cool on a cooking rack, loosely covered with a kitchen towel.