Cook the streaky bacon over medium heat until crispy. Drain the bacon on a paper towel and when they have cooled, crumble the bacon into small pieces. Mix the bacon, cheese and parsley together. Set aside.
Preheat the oven to 200 degrees Celsius. Line baking sheets with baking parchment.
Combine water, butter, sugar and salt in a pot. Heat the mixture over high heat, stirring occasionally with a wooden spoon, and bring it to a rolling boil. Add in all the flour at once, turn off the heat and stir quickly with the wooden spoon to mix in all the flour.
Once the flour has been mixed in, turn on the heat to medium-low and continue mixing with the wooden spoon until the mixture forms a soft dough and that you can see a layer of dough at the bottom of the pot, about 2 to 3 minutes. Remove from heat and transfer the dough into a mixing bowl and let cool slightly so that the eggs don't cook when they are added.
Add in the eggs, a little at a time, beating well (either with an electric mixer or a wooden spoon) until the egg has been fully incorporated before adding the next bit of eggs. The choux pastry is ready when you use a spatula to scoop the choux up and after majority of the choux falls back into the bowl, the remaining choux "hangs" on the spatula and forms a "V" shape. Stop adding anymore eggs once this consistency has been reached. Use a rubber spatula and fold in the bacon, cheese and parsley.
Pipe or scoop small mounds of choux pastry (about 1 to 1.5-inch in diameter or 1 teaspoon per mound) onto the baking sheet, leaving 2 inches between each mound of choux. Dip a pastry brush into the beaten egg (egg wash), and brush it over the choux, smoothing down any tips poking out.
Bake the gougères for 10 minutes at 200 degrees Celsius. Lower the heat down to 175 degrees Celsius and continue baking for 20 minutes. Remove the gougères from the oven. Hold a gougère with a clean and dry tea towel and use a sharp knife to make a slit on the side. Return the gougères back to the oven and continue to bake for another 5 to 10 minutes, until the top is golden-brown and the crust is crisp.
Turn off the oven, leave the oven door ajar and let the puffs cool in the warm oven for 30 minutes. Serve warm or, if preferred, let them cool completely on a wire rack before filling it.