The eclairs:
In a thick-bottomed saucepan, bring the water, milk, butter, salt, and sugar to a boil.
When the mixture reaches a boil, pour in the flour all at once and stir vigorously with a wooden spoon for 1 minute, until a ball of dough forms and detaches completely from the bottom of the saucepan.
Pour the dough into the mixer bowl, fitted with the whisk, then add the eggs one by one, whisking quickly. The choux pastry should have a smooth consistency, but not be too soft.
Put the dough in a pastry bag fitted with a smooth tip.
Preheat the oven to 220 C (425 F).
Place 12 strips of dough on a baking sheet lined with parchment paper or a silicone mat.
Bake for 15 minutes, then reduce the oven to 190 C (375 F) and continue baking for 20 minutes.
Remove the eclairs from the oven and let cool on a wire rack.
Orange mayonnaise:
In a bowl, whisk together the egg yolks, mustard, salt, and pepper.
Pour in the oil in a thin stream, whisking continuously.
When the oil is incorporated, whisk more rapidly for 30 seconds, then add the vinegar (or lemon juice). Season to taste, then add the reduced orange juice and mix well.
Refrigerate.
Assembly:
Using a flexible knife, peel 4 oranges. When they are peeled, remove the orange segments (suprèmes) by passing the knife between the membranes and reserve them in a bowl.
Using a serrated knife, open the eclairs lengthwise, but without cutting them in half.
Mix half of the orange-flavored mayonnaise with the arugula and distribute it inside the eclairs.
Dip the shrimp into the remaining mayonnaise and place 3 in each eclair.
Place at least 2 orange segments in each eclair.
It’s ready, you can serve.
Count 2 eclairs per person.