Gougères with Migneron de Charlevoix:
In a thick-bottomed saucepan, bring the water, milk, butter, salt, and sugar to a boil.
When the mixture is boiling, add the flour all at once and stir vigorously with a wooden spoon for 1 minute, until a ball of dough forms that detaches completely from the bottom of the saucepan.
Pour this ball into the mixing bowl, fitted with the whisk, then add the cheese and mix.
Add the eggs one at a time, beating quickly. The dough should have a smooth consistency, but it should not be too soft.
Put the dough into a pastry bag fitted with a round tip.
Preheat the oven to 220°C (425°F).
Make small heaps of dough, about 1 inch (2.5 cm) in diameter, on a baking sheet lined with parchment paper or a silicone mat.
Mix the egg yolk and milk, and brush the gougères with the mixture.
Bake for 15 minutes, then reduce the oven to 190°C (375°F) and continue baking for 20 minutes.
Remove the gougères from the oven and let them cool on a wire rack.
Lobster salad:
Shell the lobsters and crumble the meat. Mix with all the other ingredients in a bowl. Cover and refrigerate to allow the flavors to develop.
Assembly:
Cut the gougères in half, fill the bottom half with lobster salad, and cover with the top half of the gougère.