In a medium saucepan put milk, water, sugar, butter and salt and heat to a strong boil.
Add flour and stir while cooking, until it turns into a lump of dough.
Transfer the dough to the bowl of an electric mixer with a paddle attachment and mix on medium speed for 2-3 minutes until it cools down a little.
Add the eggs gradually while beating until dough is elastic and smooth. Check the readiness of dough by creating a "trail" with a wooden spoon in the center of the dough - if the track remains stable, add some eggs, and if it closes a bit - the dough is ready. It is important not to add too many eggs to the dough or it may become too soft and ruined.
Transfer the dough to a pastry bag fitted with a round 2 cm piping tip. On a baking tray lined with baking paper pipe small cream puffs (about 3-4 cm in diameter). It's important to leave some space between the creampuffs.
Bake for about 12 minutes. Then lower the temperature to 180c degrees and open the oven door slightly, by sticking a wooden spoon in it.
Bake the puffs in this way for 5-7 minutes, until they are golden.
Cool completely before filling.
Make a small hole at the bottom of each creampuff.
Vanilla and rum pastry cream:
In a small saucepan put milk, sugar and vanilla and bring to a simmer.
In a separate bowl, whisk egg yolks and cornstarch until blended. If the mixture is too thick - add a teaspoon of cold water.
When the milk mixture is boiling remove from heat and add about 1/3 of it into the yolk mixture while vigorous whisking. When blended, return into the pan with the remaining milk and mix.
Continue to cook over medium-low heat, while whisking constantly, until a very thick pastry cream forms.
Transfer the cream into a sealed container and cover its top with plastic wrap to avoid crust from forming. Cool completely in the refrigerator.
Transfer the cold cream into a bowl and mix well with a whisk until it returns to the original texture. Add rum and continue to mix until uniform.
Transfer the cream into a pastry bag with a 1 cm round piping tip and fill the puffs.
Garnish with powdered sugar and serve.
• Keep the cream puff in a closed container in the refrigerator for up to 3-4 days, but they are at their best on the day or two after preparation.