1/4 cup warm water
1/4 cup warm milk (whole milk is best)
3 teaspoons active dry yeast
2 3/4 cup all-purpose flour
1 1/2 teaspoons salt
4 eggs at room temperature, separated
3 tablespoons sugar
1 1/2 sticks unsalted butter at room temperature
1 tablespoon vegetable oil
In a glass mixing bowl or measuring cup, combine the warm water, warm milk, and active dry yeast. Set aside for 8 to 10 minutes.
Add the yeast mixture to the bowl of a stand mixer with a paddle attachment, and add the flour and salt. Mix until well combined, about 2 minutes.
Add 3 of the eggs, 1 at a time, mixing well after each addition.
Add the sugar and beat 3 to 4 minutes, until the mixture is smooth.
With the mixer running on a low speed, add the butter 1 tablespoon at a time.
Once all butter is added, change the attachment to a dough hook.
Increase the speed to medium-high, and knead until smooth and elastic, about 8 to 10 minutes.
Remove the dough from the mixer and shape it into a ball.
Pour the tablespoon of oil into a large bowl and turn the dough over in it until fully coated.
Cover the bowl with plastic wrap and set aside in a warm place to rise for 90 minutes, or until doubled in size.
Pull the dough away from the edges of the bowl, then re-cover and transfer to the refrigerator.
Keep covered in the refrigerator overnight.
Heat the oven to 400 F.
Smear a small amount of water on a work surface, and spread out the dough.
Divide the dough into 12 pieces, and roll them gently into balls between your hands, occasionally dipping your hand in water to limit stickiness.
Grease a muffin tin with butter or cooking spray, and place each ball in the tin.
In a small bowl, whisk the final egg and gently brush over each of the buns.
Bake for 15 to 20 minutes, or until just turning golden brown.
Allow to cool at least 10 minutes before transferring to a wire rack to cool completely.