In the bowl of a stand mixer, combine flour, sugar, yeast, and salt. Add cold milk, cold water, and softened butter. Mix on low for 5 minutes. Using cold liquids prevents the yeast from over-fermenting early on.
Shape dough into a rough rectangle, wrap in plastic, and refrigerate for at least 1 hour. This relaxes the gluten.
Pound cold European butter between parchment paper into an 8x8 inch square. The butter must be pliable but cold (around 60°F) to prevent melting.
Roll chilled dough into a 16x8 inch rectangle. Place the butter block in the center and fold the dough edges over to seal the butter completely.
Roll encased dough to 24x8 inches and fold into thirds like a letter. Chill for 45 minutes. Repeat this process two more times for a total of three turns to create layers.
Roll dough into an 8x12 inch rectangle, cut into three strips, and braid or roll them. Place in a parchment-lined 9x5 loaf pan.
Proof at 75°F for 2 hours until doubled. Do not exceed 78°F or butter will melt.
Brush with egg wash. Bake at 400°F for 15 minutes, then lower to 375°F and bake 25-30 minutes more. Cool completely before slicing to protect the layer structure.
