In a small bowl, stir together the warm milk, warm water, sugar, and cuttlefish ink until well mixed and dissolved. Add the yeast and give it a quick stir, set aside, and let activate while preparing the rest of the ingredients.

To the bowl of an electric stand mixer, add the flour, salt, and eggs.

Add the activated yeast mixture and stir together with a wooden spatula until the flour is mostly incorporated.

Add a dough hook to the mixer and knead on low speed until a sticky dough forms. Add the butter 1 tablespoon at a time until each tablespoon is well incorporated. Continue kneading the dough on low for 5 minutes.

Transfer the dough to a well-oiled bowl, coating all sides of the dough, and cover with a tea towel. Let rise in a warm spot for 1 1/2 hours.

Preheat the oven to 350°F. Prepare 2 aluminum baking sheets with parchment paper and set aside.

Transfer the dough to a clean and lightly oiled workspace. Using an oiled bench knife, divide the dough into 8 equal parts. Oil your hands and shape the dough sections into rounds by pulling the sides of the dough and pinching to secure them into the center. Continue this process to create surface tension on the other side and as close to a round shape as you can manage before carefully flipping over and transferring to the parchment paper baking sheet.

Repeat for all 8 dough sections, leaving space between each on the sheets. Let rise for 30 minutes uncovered.

Bake both sheets for 25 minutes before transferring to a cooling rack.

Store the buns in an airtight bag if not eating them right away. You can slice and toast them to give them a crispy outer texture, extra yum!