Preheat oven to 475°F. Prepare 2 baking sheets by lining them with parchment paper. Also prepare a pastry bag by adding a plain ½” tip.
In a medium saucepan over medium heat, add milk, water, butter, 1 tbsp sugar, and salt, and bring to a boil, stirring occasionally. Add flour in the pot, all at once, and begin to stir very quickly. A ball of dough should form relatively quickly. Continue cooking, stirring vigorously, until a dry film begins to form on the bottom and sides of the saucepan. Remove from heat.
Place dough into a stand mixer, fitted with the paddle attachment, and beat for about 30 seconds to a minute, to cool the dough down. Add one egg and beat until completely incorportated (the dough should look dry again). Continue adding eggs one at a time, ensuring that each is completely incorporated before adding the next, scraping at the sides of the bowl occasionally. After the 4th egg, place remove paddle from mechanism and place deep into the batter, if the batter forms a nice “V” shape off the paddle, it is ready. If the batter still looks thick and does not form a nice “V” then add another egg. Dough should be thick and sticky, but also shiny and smooth.
Add dough to the piping bag, and pipe directly onto parchment lined baking sheets. Pipe about nine 2” rounds per baking sheet (about 18 total). If your piped rounds have peaks, dip your finger into water and press down to flatten the peaks.
(Optional) For cream puffs that are more “perfect” in shape, freeze the cream puffs for 1 hour.
Add an egg and water to a bowl and whisk together to form an egg wash. Using a pastry brush, brush over the piped rounds. Place into the 475°F oven, for exactly 1 minute then immediately turn the oven off. After 9 minutes, turn the oven back on to 350°F, and bake for an additional 10 minutes. Rotate pans and bake for another 10 minutes, or until the cream puffs are puffed and golden (~ 30 minutes total baking time). To ensure the cream puffs are finished, remove one of the oven and check if it deflates within 45 seconds – if it deflates they are not finished.
When done, turn the oven off, and crack the oven 1/3 way open. Allow cream puffs to cool for 30-45 minutes in the cracked oven. Then, remove from oven and allow to cool completely before filling.