In a medium saucepan, combine the 3/4 cup water, 5 tablespoons unsalted butter, 1/2 teaspoon salt, and 1/8 teaspoon black pepper. Bring the mixture to a gentle boil over medium heat, stirring occasionally to melt the butter.
Once the mixture is boiling, remove the saucepan from the heat and quickly stir in 1 cup plain flour. Mix vigorously until the dough comes together and forms a ball, pulling away from the sides of the pan.
Allow the dough to cool for about 5 minutes. This is essential to avoid cooking the eggs when you add them in the next step.
In a mixing bowl, whisk together the 4 large eggs. Gradually add the eggs to the dough, one at a time, mixing well after each addition. The dough should be smooth and glossy.
Once all the eggs are incorporated, fold in the 3/4 cup grated mozzarella cheese, 1/2 cup grated Parmesan cheese, and 1/4 teaspoon minced Italian parsley. Ensure the cheese is evenly distributed throughout the dough.
Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper. Using a spoon or a piping bag, drop tablespoon-sized mounds of dough onto the prepared baking sheet, spacing them about 2 inches apart to allow for rising.
Place the baking sheet in the preheated oven and bake for 20-25 minutes, or until the gougères are puffed and golden brown. Avoid opening the oven door during the first 15 minutes to ensure they rise properly.
Once baked, remove the gougères from the oven and let them cool slightly on a wire rack. Serve warm or at room temperature, and enjoy these delightful cheese puffs with friends and family.