Preheat the oven to 400ºF. Line a baking sheet with parchment.
In a saucepan, heat together the water, milk butter, salt and sugar. Bring the mixture to a rolling boil.
Remove the pan from the heat and dump in all the flour. Quickly mix it in with a wooden spoon, then place the saucepan back on the heat to dry the dough. The dough will form a uniform, slightly shiny mass when it's cooked enough.
Transfer the dough to the bowl of the stand mixer and beat with the paddle attachment til it's cool.
Add 3 eggs at once, and beat them in until they have completely disappeared.
Add the 4th egg and beat it in. If the pâte à choux doesn't have a pipeable consistency (soft but firm) and doesn't form a "bec d'oiseau" (a curved beak shape on the end of a spoon), then add another half egg.
Scoop the pâte à choux with a ¾ oz scoop (find it on Amazon) onto the prepared baking sheet, spacing an inch apart. Brush with the remaining half egg, and then bake for a good 15 min at 400ºF until the choux have puffed and are starting to brown, quickly open the door just a crack to release steam, then shut it and lower the temperature to 375ºF for another 10 minutes to finish the baking.
Transfer to a rack to cool.
To make the whipping cream and assemble
Whip the cream to soft peaks with the whisk attachment of a stand mixer.
Add the icing sugar and vanilla, and finish whipping.
To a pipping bag fitted with the Wilton 1M piping tip (from Amazon), streak a little raspberry jam down the inside and then fill with whipping cream.
Slice the cooled choux puffs to open them and pipe the cream in the hole of the base. Finish with the top half and sprinkle with icing sugar before serving.