In a large bowl, combine wheat flour type 405, wheat flour type 550, heaped teaspoon of sugar, salt, and yeast. Add the warm water, warm milk, and liquid butter. Knead for about 8–10 minutes until the dough is smooth and elastic. Cover with a damp cloth and let rise in a warm place for about 30 minutes until roughly doubled in size. Knead again for about 1 minute. Preheat the oven to 50°C / 120°F for proofing.
Shape the dough into round rolls. Pour the 4% lye (soda) solution into a medium bowl to a depth of about 1 cm. Wearing household gloves, dip each roll into the lye and turn for about 10 seconds to coat all sides. Caution: lye is corrosive—wear protective gloves and avoid skin contact.
Place the lye-dipped rolls onto a baking sheet lined with baking foil (lye-resistant). Let rise in the preheated low oven (50°C / 120°F) for about 10–15 minutes.
Remove from the oven. Wearing household gloves, lightly brush the surface of each roll again with lye solution. Using a sharp knife or scissors, cut or slash across the top of each roll. Choose one topping: either sprinkle with coarse salt, or carefully pull the roll apart along the cut and fill with grated cheese.
Increase the oven temperature to 230°C / 446°F. Place the rolls in the oven and bake at 230°C / 446°F for the first 5 minutes, then reduce the heat to 200°C / 392°F and bake for about 25 minutes more until deep golden brown (approximately 30 minutes total). Optional: place a bowl of water on the bottom rack of the oven during baking for softer rolls.
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