In a small bowl, combine warm milk, yeast, and a pinch of sugar. Let sit for 5-10 minutes until foamy.
In a stand mixer with a dough hook, mix bread flour, sugar, and salt. Add yeast mixture and mix on low until a shaggy dough forms. Knead on medium for 5 minutes.
With mixer on low, add softened butter one tablespoon at a time. Once incorporated, knead on medium for 8-10 minutes until smooth and elastic.
Shape dough into a ball, place in a greased bowl, cover, and let rise until doubled, about 1-1.5 hours.
Meanwhile, make custard: whisk egg yolks, sugar, and vanilla bean paste in a saucepan. Whisk in milk and cornstarch. Cook over medium heat, stirring constantly, until thickened. Remove from heat, stir in butter, and chill until firm.
On a floured surface, roll dough into a 12x16-inch rectangle. Spread cooled custard evenly, leaving a 1-inch border. Sprinkle with chocolate chips.
Roll dough tightly from a long side into a log. Pinch seam to seal. Cut log in half lengthwise, twist halves together with cut sides up, and place in a lined 9x5-inch loaf pan.
Cover and let rise until puffy, about 45 minutes to 1 hour. Preheat oven to 350°F (175°C).
Brush top with egg wash. Bake for 25-30 minutes until deep golden brown and internal temperature reaches 190°F (88°C). Cool in pan 10 minutes, then transfer to a wire rack to cool completely.