Add the active dry yeast and 1 tablespoon of sugar into 1 cup of lukewarm milk.
Wait for the yeast to activate (about 10 minutes).
Add 3 cups of sifted bread flour to the mixer bowl.
Add 2 tablespoons of sugar and ½ tablespoon of salt to the flour.
Mix the flour and add in 8 tablespoons of melted butter.
Crack 3 eggs into a separate bowl and add squid ink to it. Stir well.
Add the squid ink mixture, then the activated dry yeast to the flour.
Mix with the dough hook on medium speed for at least 10 minutes.
Put some flour on the working top and transfer the dough to it.
Work the dough using your fingers.
Put it in a bowl coated with some olive oil.
Cover the dough with plastic wrap or cheesecloth.
Let it proof until it doubles in size (about 2 hours)
Press the air from the dough using your knuckles.
Lightly knead the dough to form a log shape and divide it into 10 to 12 pieces.
Shape each piece of dough into a ball.
Put the dough balls on a lined baking sheet.
Cover the buns with plastic wrap and let them rest for 60 minutes.
Prepare the egg wash using 1 whole egg and two tablespoons of water. Mix well.
Brush the buns with egg wash and top them with sesame seeds.
Preheat the oven to 375 degrees F.
Bake the buns for 15 to 18 minutes.
Once cooked, take them out of the oven and let them cool down.