In a large saucepan, combine the water, milk, butter, and salt. Bring to a boil over medium heat. When the mixture is boiling, add the flour all at once and stir vigorously with a wooden spoon until the mixture pulls away from the sides of the pan. Continue to cook and stir the mixture for about 1 minute to eliminate excess moisture. Depending on whether you used an aluminum or a nonstick pan, a thin layer of dough may stick to the bottom of the pan: this is normal. Take off the heat. At this point, the dough mostly comes together and rolls away from the sides of the pan when stirred.
Transfer to the bowl of a stand mixer, or to a large mixing bowl if you’re using a hand mixer, and let cool for 5 minutes, stirring occasionally to allow the steam to come out.
Set the mixer to medium speed, and beat the eggs in one at a time, making sure each egg is well incorporated before adding the next. Also scrape the bowl down between each egg addition. Every time you add an egg, the dough will separate and look like a curdled mess, but it will then come back together in a really sticky, yet somewhat crumbly way. The dough will keep on getting smoother as you add more eggs. The dough is done when it is smooth and elastic, not dry. It will be very thick and sticky.
Using a spatula, fold in the parmesan cheese and black pepper until well incorporated.
Use a small cookie scoop or a tablespoon to create the puffs. Drop the dough on the parchment paper, spacing each about 3 inches (7.5 cm) apart. Using damp fingertips, press down any peaks of dough to create perfectly round puffs. Bake gougères until golden brown, 20 to 25 minutes, switching the position of the baking sheets halfway through baking. Using a small paring knife, pry open 1 gougère to check for doneness: the center should be slightly eggy and moist.
Transfer the parmesan puffs to a rack and let cool completely, about 1 hour. The puffs are best enjoyed the day they’re baked, but you can store them for a few hours in airtight containers before filling.
FOR THE SMOKED SALMON MOUSSE
Place the salmon in the bowl of a food processor. Pulse until coarsely chopped. Add the cream cheese, heavy cream, lemon juice, and coriander, and process until creamy and light. If the mousse seems too thick, add more cream, 1 teaspoon (5 ml) at a time until you reach the right consistency. Season with salt and pepper to taste. Store in an airtight container until ready to use.
Transfer the smoked salmon mousse to a pastry bag fitted with a closed star tip. Using a bread knife, saw off the top of each puff. Fill each puff, then replace the cap over the mousse. If desired, add a dot of filling over each cap, then decorate with a fresh coriander leaf. Set the puffs on a serving plate and serve immediately, or refrigerate, uncovered, for up to an hour before serving. (Always add the fresh herb garnish right before serving or it will wilt during storage.)
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