Make the Cream Filling (Diplomat Cream):

1. Add sugar, cornstarch, and salt to a medium pot and whisk together. Whisk in egg yolks, whole egg and milk until fully combined. 
2. Turn on the heat to medium and cook the mixture, whisking constantly, and occasionally taking a spatula and scraping up any thickened cream in the edges of the pan. Cook until the pastry cream has completely thickened and large bubbles are forming and popping, about 4-6 minutes.
3. Remove from heat; immediately pour the thickened mixture through a fine mesh strainer into a bowl, using a spatula to push all the pudding out while leaving behind any bits of cooked egg.
4. Whisk in the butter and the vanilla extract (or vanilla bean) into the pastry cream until fully combined.
5. Transfer the pastry cream into a shallow bowl and place a piece of plastic wrap directly on the top of the cream. Let cool at room temperature for 30 minutes before chilling in the refrigerator for at least 2 hours.
6. Once chilled, whisk together the pastry cream to loosen it up..
7. Add the heavy cream to a large bowl (or an electric mixing bowl) and whip until stiff peaks form. Add pastry cream to the bowl with the whipped cream and gently fold together. 
8. Transfer the finished diplomat cream to a piping bag and store in the refrigerator until ready to use (no more than 1 hour ahead).

Make the Choux Pastry:

1. Add water, milk, butter and salt to a medium pot. Turn the heat on to medium, and stir the mixture while the butter melts. Once the butter is melted, remove from the heat briefly to stir in the flour. Return the pot to the heat, and cook this flour mixture while stirring and mashing the dough up against the bottom of the pot, until it forms itself into a ball, and the dough has reached a temperature of 175º, about 1 to 2 minutes.
2. Let the dough cool slightly until it reaches a temperature below 150ºF, about 5-10 minutes (see notes about alternative methods that are less labor intensive).
3. Whisk eggs together in a liquid measuring cup. Pour about ¼ of the whisked eggs into the dough, and vigorously stir the dough together with a wooden spoon until the egg is fully mixed into the dough. Repeat this process of adding in about ¼ of the eggs, while mixing, two more times. When the last remaining ¼ of the eggs are left, add in a tablespoon of the egg at a time, and mix together until the dough looks shiny and drapes off a spoon to forms a “V” shape. Do not add in so much egg that the mixture is very loose. You may not use all of the whisked eggs, and can use any leftover as an egg wash.
4. Transfer the mixture to a piping bag fitted with a small circular piping tip (either ¼”-½” opening).

Piping and Bake:

1. Preheat the oven to 425ºF and place a rack to the lower middle part of the oven.
2. Pipe 4 tiny mounds of choux on each corner of the baking tray, and then place a piece of parchment on top and press it to the choux pastry (this keeps the parchment in place).
3. Pipe 1-½” mounds of dough, about 1” apart on the baking sheet. With a wet finger, gently press down on any of the dough that has formed a peak. Gently brush an egg wash on the choux buns (or use any leftover whisked egg here).
4. Place the choux pastry on the middle rack and immediately lower the temperature to 375ºF and bake for 30 minutes, or until the choux is lightly golden all over.
5. Shut off the oven, crack open the door and let them cool for 15 minutes in the oven, to dry out.
6. Remove from the oven. If desired, poke a hole in each puff to let the steam escape. This is optional.

Fill:

1. Slice open the baked choux buns horizontally. Pipe in the diplomat cream and add in a berry, if desired. Place the choux bun top back on the puff, and generously dust the choux puffs with powdered sugar. Cream puffs can keep for up to 4 hours in the refrigerator, but they’re best when served right away.