In a large bowl, combine sourdough starter, lukewarm milk, egg, sugar, salt, and instant yeast. Mix until combined, then gradually add flour and softened butter. Knead until smooth and elastic, about 6 to 8 minutes with a mixer or 10 minutes by hand.

Cover and let rise at room temperature for 3 to 4 hours until visibly puffed.

While the dough rises, pound the cold butter between two sheets of parchment paper into a 7x7 inch square. Refrigerate until firm but still pliable.

On a lightly floured surface, roll the dough into a 10x10 inch square. Place the butter block diagonally in the center and fold the dough corners over it to fully enclose.

Roll into a 10x20 inch rectangle and fold into thirds like a letter. Wrap and refrigerate for 30 minutes. Repeat this process two more times, chilling for 30 minutes between each turn.

After the final chill, roll the dough into a 12x20 inch rectangle. Sprinkle chocolate chips evenly over the surface. Fold the dough over to enclose the chips and shape into a loaf. Place in a greased loaf pan.

Cover and proof at room temperature for about 2 hours until puffy and nearly doubled.

Preheat oven to 375°F (190°C). Bake for 30 to 35 minutes until deep golden brown. If the top colors too quickly, tent loosely with foil.

Cool in the pan for 10 minutes, then transfer to a wire rack. Cool for at least 1 hour before slicing.