Whisk active sourdough starter, warm milk, and sugar. Add bread flour and fine salt. Knead for 5-7 minutes until smooth and elastic. Let ferment covered for 3-4 hours until 50% larger.

Pound the cold European butter between parchment paper into a 6x6-inch square. Chill for 15 minutes.

Roll fermented dough to a 12x6-inch rectangle. Encase the butter block inside the dough, seal edges. Roll to 18 inches long, perform a letter fold. Chill 45 minutes. Repeat this folding and chilling process two more times.

Roll dough to 10x14-inches. Layer thick, folded slices of cooked pink ham and shredded gruyere down the center. Cut diagonal strips on the sides and criss-cross them over the filling.

Transfer to crinkled parchment on a dark metal baking sheet. Brush with egg wash and sprinkle with coarse white sea salt flakes and tiny green dried parsley specks. Bake at 400°F (200°C) for 35-40 minutes until the crust is highly blistered, deep golden-brown, and shiny.