Bring the water, butter and salt to a boil in a medium saucepan. Add the rosemary and thyme. Remove the pan from the heat and add the flour. Return the pan to medium-high heat and stir until batter pulls away from the side of the pan. Scrape the batter into the bowl of a standing mixer and mix a few times with the paddle to cool the dough down a touch. This will prevent the eggs from scrambling when they hit the hot dough.
On low speed, add the eggs one by one; after each egg is added, increase the speed to medium and beat until the egg is incorporated. The eggs can also be beaten in by hand. Beat well after all eggs have been added. Add the Gruyère and Parmesan and beat until well incorporated.
On a parchment-lined sheet pan, using a pastry bag, pipe the batter into half dollar-sized rounds. The batter can also be scooped into mounds with a tablespoon. Freeze the puffs.
Preheat oven to 450°. Egg wash the puffs straight from freezer. Bake for 40 minutes, then reduce heat to 400° and bake until puffed and golden. Serve warm.