Mix together the yeast, flour, and salt in the bowl of a stand mixer fitted with a dough hook attachment.
With the mixer running on "stir" speed, pour in the water and milk. Then add in the honey, egg, egg yolks, and vegetable oil. Increase speed to medium and knead for 5 to 6 minutes until the dough completely pulls away from the bowl and is no longer sticky to the touch.
Shape the dough into a ball and transfer to a large greased bowl and cover with a damp dishcloth and proof (rise) for 1 hour.
Remove the dough from the bowl with the top right side up on a lightly floured surface. Pull the edges of the dough from 4 points, flip, and work in a circular motion on the counter to seal, then place back in the bowl. Cover the dough with the damp dishcloth again and proof for an additional hour.
Remove from the bowl and evenly divide the dough into the number of braids you want, I like to use 4. Shape the dough into logs. Cover the dough logs with the damp dishcloth and let the rest for 20 minutes.
Roll each log out into 1½-inch strips of dough, working from the center and rolling with your hands, tapering the dough at the ends. Secure one end of dough strips together and braid. Place bread on a greased baking sheet.