In a large mixing bowl, combine 2 1/4 cups of the flour, sugar, salt, and yeast. Whisk until well-incorporated.
In a microwave-safe bowl, combine butter, water, and milk. Microwave until butter is melted and the temperature of the mixture is between 110 to 115. If too hot, cool down to the right temperature before proceeding to the next step.
Add the butter mixture to the dry ingredients. Using a wooden spoon, stir the until moistened.
Add the egg and mix briefly.
Add the remaining 1/4 cup of flour in increments. Once the dough gathers into a rough ball and pulls from the sides of the bowl, stop adding flour. You probably won't need the entire 1/4 cup.
Turn the dough over in a floured board. Using hands, knead for about 7 to 10 minutes or until the dough is smooth and no longer sticky.
In a bowl, place dough and cover with a clean kitchen towel. Let rest for ten minutes.