Add All-purpose flour, instant dry yeast, salt, and sugar to your kitchen mixer and mix for a few seconds. Don't worry if you don't have one of these fancy kneaders, just use a big bowl. Melt the butter. Add milk and melted butter to the dry ingredients.
Knead dry and wet ingredients together until you have a smooth, stretchy dough. If you use a kitchen aid or similar, start on slow speed for a while, then turn it up to a fast rate for the last few minutes. If you knead by hand, do so for about 15-20min. I know it's a workout, but to achieve a light and airy bread, you need to work that dough until it is nice and smooth to achieve a light and airy bread.
Form the dough into a ball. Place it in a big, lightly floured bowl and cover it up with a wet kitchen towel, or something similar, to keep it from drying out. Let it rest to rise for at least 1 ½ hours.
Line a baking sheet with parchment paper or a silicone baking mat. Take risen dough carefully out of the bowl and onto a lightly floured surface. Cut it into two halves. If you want to make a smaller loaf, just cut it twice to get four equal pieces.
Roll each dough piece into long strands. You need two strands of equal length to braid. Lay one strand on top of the other so that it looks like a plus sign. Make sure the horizontal strand is the bottom strand. Take the bottom strand and hold it on both ends, fold it from the left over the top strand to the right, below the other side of the horizontal strand. Then take the right side of the bottom strand and fold it over the just-placed bottom strand and over the top strand to the left. Then take the original vertical top strand, hold it on both ends, and cross them above the previously bottom strand (left side over the right side). Repeat until you use up all of the strands. Preheat the oven to 392 Fahrenheit or 200 Celsius
Crack one egg into a small bowl and whisk it slightly. Brush the whole bread with the egg wash using a food brush. Ensure you get every part of the dough, or it will bake with an uneven color. Let it rest for another 30min. After the second rest period, brush the Zopf one more time with egg wash.
Bake for 30-40min (if you have one large loaf) or 20-25min (if you have two small loaves). Let it cool for a little bit before you cut into it.