Add warm milk to a large bowl with instant yeast and honey. Whisk until the honey is dissolved and the yeast is combined.
Add the melted butter, egg, sourdough discard, all-purpose flour, and salt to the same bowl. Stir well with a wooden spoon until a shaggy dough forms.
Turn this rough dough out onto your countertop and begin kneading. You will knead for about 4 to 5 minutes until the dough becomes smooth.
Form the dough into a ball, and place it into a lightly greased, large glass bowl. Cover with a tea towel or plastic wrap, and set it in a warm spot to rise until doubled in size. This will take approximately 90 minutes, depending on the temperature.
Prepare your baking sheets by lining them with parchment paper.
With the dough on a hard work surface, begin dividing it into 8 equal parts.
Shape each dough piece into bun shapes by pulling the top smooth and tucking the sides underneath. You'll space them out, 4 buns per baking sheet.
Cover and let the dough rise a second time until doubled in size. This may take around 60 minutes.
With the second rise completed, preheat your oven to 350 degrees Fahrenheit.
Prepare the egg wash by whisking the egg yolk with the water.
Brush the top of the dough with the egg wash, then sprinkle with sesame seeds or your topping of choice. The egg wash gives the buns a beautiful glossy crust.
Bake the buns for 20 to 25 minutes, until they are glossy and golden brown.
Cool completely before slicing and serving. You can use a cooling rack, or simply cool on the baking sheet.