Make the tangzhong: In a small saucepan, whisk together 2 tbsp bread flour and 3 tbsp whole milk until smooth. Place over medium-low heat and stir constantly until it thickens into a paste that holds its shape when you lift the whisk, about 2 minutes. Remove from heat and let cool for 10 minutes.
Combine dry ingredients: In the bowl of a stand mixer, whisk together 2 1/2 cups bread flour, 1/3 cup sugar, 2 1/4 tsp yeast, and 1 tsp salt.
Add wet ingredients: Add the cooled tangzhong, 1/2 cup warm milk, and 1 egg. Mix on low with the dough hook until a shaggy dough forms, about 2 minutes.
Knead and add butter: Increase speed to medium and knead for 5 minutes. Add 3 tbsp softened butter one tablespoon at a time, letting each incorporate fully. Knead another 3-4 minutes until the dough is smooth, soft, and slightly tacky. It should stretch into a thin windowpane without tearing.
First rise: Shape the dough into a ball and place in a lightly oiled bowl. Cover with plastic wrap and let rise in a warm spot for 1 hour, or until doubled in size. (Oven trick: heat to 170°F for 2 minutes, turn off, place dough inside with door cracked.)
Divide and flatten: Punch down the dough and turn it onto a lightly floured surface. Divide into 12 equal pieces (about 70g each). Flatten one piece into a 3-inch round.
Add chocolate and seal: Place a small handful of chopped chocolate in the center of each round. Pull the edges up and pinch firmly to seal. Roll seam-side down to create surface tension.
Arrange in pan: Place buns seam-side down in a buttered 10-inch cast iron skillet or 9x13 baking dish. Cover loosely with plastic wrap and let rise 45 minutes until puffy and doubled, touching each other.
Preheat and egg wash: About 15 minutes before the rise is done, preheat oven to 350°F. Whisk 1 egg with 1 tbsp milk. Gently brush the tops of the buns with egg wash.
Bake: Bake for 22-25 minutes, rotating pan halfway through. Buns are done when deep golden brown and internal temperature reaches 190°F.
Honey butter finish: While baking, melt 2 tbsp butter with 1 tbsp honey. As soon as buns come out of the oven, brush with honey butter. Serve warm or at room temperature.