Preheat the oven to 350°F. Line 2 baking sheets with parchment paper.

Make the cheese puffs: In a medium saucepan set on medium-high heat, combine the water, milk, butter and salt and bring to a boil. Add the flour all at once and stir it with a wooden spoon until a smooth dough forms. Turn the heat to low and stir until it dries out and pulls away from the pan, about 1 - 2 minutes. Transfer the dough to the bowl of a stand mixer fitted with the paddle attachment. On low speed, add the eggs one at time, making sure each egg is fully incorporated before adding the next. (As you add the eggs, the dough will split, but as you continue to mix, the dough will come back together). The finished dough will be shiny, smooth, and quite thick at this point.

Add the gruyere cheese and black pepper and fold in with a rubber spatula. Transfer the dough to a pastry bag fitted with a 1/2 inch smooth round tip. Pipe 1-inch mounds onto the baking sheets, about 2 inches apart. Alternatively, you can use a tablespoon to make 1-inch rounds. In a small bowl, mix together an egg with one teaspoon water. Lightly brush each mound with the egg wash and top with a sprinkle of everything seasoning. Bake for 20-30 minutes until the gougères have puffed up and turned golden brown. They should feel light in weight for their size. If they feel heavy, put them back in the oven for a couple of minutes.

Make the filling: While the pastries are baking, make the filling. Add the cream cheese, goat cheese, cream, salt and pepper to the bowl of a stand mixer fitted with the whisk attachment. On low speed, mix until the cheese and cream are combined and smooth. Turn the speed to medium and whip until the mixture becomes lighter in texture, about 2 minutes. Add the scallions and dill and stir on low until just combined. Transfer the cream cheese mixture to a pastry bag fitted with a 1/4 inch smooth round tip.

Let the baked gougères sit until cool enough to handle, then make a small hole in the side of the choux with a sharp knife and pipe in 1/2 to 1 tablespoon (depending on how filled you want each puff to be) of the cheese filling. Serve warm or at room temperature. The filled puffs will soften after about an hour, so if you’re not serving immediately, store the pastry and whipped cheese separately and fill when ready to serve.