In the bowl of an electric mixer fitted with the dough hook attachment, stir the yeast, water, milk, sugar, 2 tablespoons of the butter, egg, and salt until well combined. Gradually add the flour and knead on medium-low speed until the dough pulls away from the sides of the bowl. Turn off the mixer and let the dough rest for 3 to 5 minutes. Continue to knead the dough on medium-low speed for another 5 minutes, or until the dough is soft and smooth. If it seems too sticky, add more flour, 1 tablespoon at a time.