In the bowl of a stand mixer or large mixing bowl, combine warm milk, water, honey, and yeast. Let sit 5–10 minutes until foamy.
Add cooled melted butter, sourdough discard, egg, salt, and 4 ¼ cups of flour. Mix on low speed (or with a wooden spoon) until a shaggy dough forms. Add up to ¼ cup more flour as needed until dough is tacky but not sticky.
Knead dough in the stand mixer for 8–10 minutes (or by hand for 10–12 minutes) until smooth and elastic.
Transfer dough to a greased bowl, cover, and let rise in a warm spot until doubled, about 1 hour.
Punch down the dough and divide into 10 equal pieces. Flatten each piece into a 3-inch round. Fold edges inward, overlapping and pinching to seal the center.
Flip seam-side down and gently rotate under your hand to smooth the top. Place on parchment-lined sheet: 1 inch apart for soft pull-apart buns, or 2–3 inches apart for classic individual buns. Slightly flatten each bun, cover, and let rise 30–45 minutes.
Preheat oven to 400°F. Brush buns with milk for a golden brown top. If you’d like seeds or seasoning, brush with milk first, then sprinkle on sesame seeds, poppy seeds, or everything bagel seasoning. Bake for 12–15 minutes until golden brown and center reaches 190°F.
Brush warm buns with melted butter if desired.