Preheat oven to 425 degrees.
Combine water, salt, and butter in a saucepan over high heat. You don’t need to stir it as it heats, just be sure that the butter melts quickly and your water doesn’t start to evaporate while you are waiting for it to melt.
Turn heat down to medium and add all flour at once. Stir with a wooden spoon for about 3 minutes until the mixture becomes cohesive, pulls away from the sides of the pan, and leaves a thin coating of flour on the sides/bottom of the pan.
Transfer to a mixing bowl and beat with a wooden spoon for about one minute to cool it down.
Beat in the eggs, one at a time, until you have added all four. You’ll know that the dough is ready when you can slide a wooden spoon down the middle and it makes a groove that slowly closes in on itself, or when it gently drops from the spoon when held sideways. If it is still too thick, you can add one egg white at a time until it comes to the proper consistency.
Add cheese and rosemary, stir gently to combine
Fill a pastry bag with a straight tip or use a large plastic freezer bag with the corner cut off. Place the opening of the bag down into a large pitcher, glass or vase. Drape the top of the bag over the sides of the opening of your vessel, and use a spatula to spoon dough into the bag. (This makes things so much easier than trying to wrangle the bag with one hand and the mixture with the other.)
Line a baking sheet with parchment and pipe out bonbon sized balls of dough. Leave a good amount of space between because they will expand. You can dip your index finger in a tiny bit of water and smooth down and little peaks that may result from the piping to ensure you have a nice round puff.
Bake in the oven for 20 minutes, rotating once during baking. Cool on a wire rack.
While preparing the gougères, allow the cheeses to soften at room temperature. Combine goat cheese, mascarpone cheese, lemon zest and parsley in a large bowl. Transfer to pastry bag or freezer bag as described above.
Once the puffs have cooled, gently break open at the side and pipe with a dollop of the goat cheese mixture. Don’t fill them full, you just want a bit of that tangy, bright surprise, about the size of a marble.