Place the water and butter into a large pot over medium-high heat and bring to a boil. Once boiling, add the sugar, salt, and flour and use a wooden spoon to mix everything to combine.
Lower the heat to medium, and cook the flour mixture for 2-3 minutes, stirring constantly to ensure the flour does not burn. The flour mixture should form a cohesive ball and create a light film on the bottom of the pot. Once cooked, transfer to a large mixing bowl and let cool for 5 minutes.
Preheat oven to 400 degrees F.
Add one egg into the flour mixture. Use a wooden spoon to mix it in to fully combine before adding another egg. The dough will split, but keep mixing and it will come back together. Continue the process until all 4 eggs have been incorporated.
Add the thyme, ¾ cup gruyère cheese, and the Parmesan cheese to the dough and mix to combine. The dough should be thick and sticky. Transfer the dough into a piping bag fitted with a round tip. Alternatively, transfer into a plastic bag and cut a 2 cm opening in one corner.
Line a baking sheet with parchment paper. Lift each corner of the parchment paper and add a small dot of batter to the pan. Place the parchment paper back on top and press it down. This will ensure the parchment paper does not move around when you are piping the gougères.
Pipe a small mound of the dough on to the parchment-lined baking sheet. Each gougère should be circular and about 4 cm in diameter. Repeat for the remaining dough, ensuring that they are spaces at least 4 cm apart.
Once the gougères are all piped, dip a pastry brush into the egg yolk and brush the tops and sides of each gougère with it. Try to create a nice dome shape with no peaks sticking out to avoid burning.
Top each gougère with the remaining gruyère cheese them bake in the oven for 22-25 minutes until they are golden brown on top. Avoid opening the oven while the gougères are baking to avoid them collapsing.
Once cooked, remove from the oven and garnish with some additional fresh thyme leaves. Serve
immediately and enjoy!