Preheat oven to 425 degrees F. Line a baking sheet with parchment paper or a silpat.In the bowl of a stand mixer, gently stir together the milk, yeast, sugar, melted butter, and egg.Add in 3 1/4 cups flour and the salt. Mix with the paddle attachment on low speed until combined then switch to the dough hook. Knead on low speed for about 5 to 7 minutes until the dough is smooth and elastic. Add in more flour within the first few minutes if it appears too wet and sticky, 1 tablespoon at a time. I needed an extra 2 tablespoons. The dough should stretch without breaking but will still be very slightly sticky to the touch.Divide the dough into about 12 pieces (about 3.5" buns) or less for larger buns, and shape into a ball. Place the dough balls on the baking sheet about 3 inches apart. Once all are rolled, cover lightly with plastic wrap and let rise for 10 minutes. Whisk the extra egg and water together and brush the dough balls with the egg wash. Sprinkle with toppings if desired. Bake for about 10 to 12 minutes until golden.Buns may be frozen in a ziploc bag or airtight container.