Heat a medium saucepan over medium heat. Preheat oven to 400°F.
Add water, milk, butter, and salt to the saucepan and whisk to combine once melted.
Measure flour onto a piece of parchment paper and "chute" the flour into the saucepan.
Using a wooden spoon, incorporate the flour into the wet ingredients and mix with force for 2-3 minutes until the flour is cooked down. The mixture should be cohesive.
Remove from heat and transfer dough to a stand mixer or large heat-proof bowl.
One at a time, add your eggs and beat into the dough with your stand mixer on medium speed (with the paddle attachment) or with your wooden spoon.
Once all eggs are incorporated, your dough should still be somewhat stiff and cling to your spoon / paddle when lifted. It's perfect when it forms a v shape. The mixture will feel thick and sturdy, not liquidy or runny at all.
The batter should now be cool. Add your parmesan cheese and black pepper and stir to combine.
Transfer mixture to a piping bag with a round tip (or just snip off 1/2 inch from the top of the plastic bag).
Line two baking sheets with parchment paper and pipe balls of dough onto each (about 12 on each sheet). They should be the size of golf balls.
At this point you can dip your finger in water and smooth your dough mountains, but I like the jaggedness of them. Sprinkle the tops with more parmesan and a little sea salt before baking.
Bake gougeres for 20 - 25 minutes until golden brown. They may start to smell burnt earlier, but it's just the cheese caramelizing.
Serve warm.