In a stand mixer with a dough hook, combine 240 g milk and 37 g honey. Stir until the honey is dissolved, then mix in the 4 g active dry yeast.
Add 150 g sourdough discard and mix to combine.
Add 400 g bread flour and mix on low speed until a dough begins to form.
Increase the speed slightly and add 28 g butter in three parts, allowing each portion to fully incorporate before adding the next.
Add 9 g sea salt and mix.
Increase speed to medium and knead for 5–8 minutes, until the dough is smooth.
Transfer to a lightly oiled bowl and cover with plastic wrap. Let rise for about 2 hours, or until doubled in size.
Divide the dough into 10 equal portions (about 83g each).
Before shaping, cover with plastic wrap and let the dough rest for 20 minutes to make it more elastic.
For hamburger buns, pull the sides of the dough into the center and pinch, then roll on the counter to create surface tension and form a round ball. Once placed on the baking sheet, gently press them down to slightly flatten.For hot dog buns, flatten each portion into a rough rectangle, then roll it up into a cylinder, pinching lightly to seal. Place shaped dough on a baking sheet about an inch apart. Once proofed, they should slightly touch.
Cover with plastic wrap and let rise for about 2 more hours until puffed up and doubled.
In the last 20 minutes of rising, preheat the oven to 350℉.
Bake for 28–30 minutes, rotating halfway through, until golden brown.
Melt the remaining 28 g butter and generously brush it over the warm buns—this is what makes them super soft and gives them that irresistible, buttery finish.
Let cool and enjoy! These buns should be fluffy, tender, and easy to pull apart.