Mix the eggs, yolk, water, milk, sugar, and starter in a large bowl (or stand mixer bowl)

Add the flour and salt to the wet ingredients and combine until you have a messy dough

Cover and let rest for 30 minutes (if your kitchen is too hot, let it rest in the fridge)

After 30 minutes start kneading the dough and once it becomes less sticky incorporate the butter

Continue kneading until the dough is very elastic and the gluten is properly developed. If necessary, let the dough rest for a few minutes once in a while

Shape the dough into a ball and place in a lightly oiled container until it doubles or almost doubles in size *See notes

When ready (if you followed my schedule, this step would be the next morning), carefully deflate the dough and divide in 8 equal pieces for medium-size buns, or 6 for larger buns

Shape each piece into a little ball and place them on your baking tray. For taller and exact shape buns you can use English muffins rings to proof and bake them

Cover the buns with lightly floured plastic wrap and let them rise until they're puffy and have grown in size (they don't necessarily need to double)

Preheat your oven a 375F/190C when the buns are almost ready (reduce the temperature a little if you have a convection oven)

Brush each bun with the leftover egg white and sprinkle with sesame seeds (optional)

Bake for 30-40 minutes or until the buns have a nice golden brown color. Time will vary depending on the oven **See notes

Once the buns are the color you like, remove them from the oven and let them cool down in a cooling rack. If you like them a bit more humid, let them cool down covered with a dry cotton cloth