In a large bowl, dissolve honey in warm water.
Stir in the sourdough starter and milk until smooth.
Add whole wheat flour, white flour, and salt, then mix into a shaggy dough.
Cover and rest 45–60 min (fermentolyse).
Mix in egg yolks until dough comes together.
Gradually add melted, cooled butter, mixing until incorporated.
Over 2 hours, perform 4–5 sets of stretch-and-folds, 20–30 min apart. Keep hands wet while stretching; lift dough until you feel resistance, then fold. Turn 1/4 turn. Repeat the stretching, folding and 1/4 turn another 3 times during each set of stretch & folds.
Let dough rise at warm room temp until ~75% larger (bulk fermentation).
Once the dough has risen, grease and flour a loaf pan (or line with parchment).
Wet your hands and counter, then gently stretch the dough into a rectangle.
Roll dough from the bottom edge into a tight log.
Tuck in ends and place seam-side down in the loaf pan.
Let rise until nearly doubled or 1–2 cm above pan rim (second rise).
Bake at 180 °C (350 °F) for 35 min, tenting with foil if browning too fast.
Brush top with melted butter, cool 15 min in pan, then transfer to a rack and cover while cooling.