Place your racks in the upper and lower thirds of your oven and preheat to 375 degrees F. Line two baking sheets with parchment paper and set aside.
In a large saucepan, combine water, and butter over medium high heat. Continue to cook, stirring, until butter has melted and mixture has come to a boil.
Reduce heat to medium low and add flour all at once, using a wooden spoon, stir vigorously until the mixture pulls away from the sides of the pan, about 30 seconds. Continue to cook and stir for an additional 1 1/2 minutes to remove more moistures. Remove from the heat and allow to cool slightly for about 3 1/2 minutes.
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Add your eggs, one at a time, beating each egg into the mixture until it is incorporated. The batter will appear to separate at first, but will then come together in a dough. Continue adding the eggs one at a time until the dough is glossy and just stiff enough to hold peaks, but pliable enough to fall softly from a spoon. This may or may not require the last egg, so monitor your dough accordingly.
On a cutting board, with the edge of a chef’s knife, smash the roasted garlic with the kosher salt to form a paste, add to the choux. Stir in 1 cup of the cheese, pepper, and rosemary until well incorporated.
Fill a pastry bag (or zipper lock bag with a snipped corner) with the dough and pipe 1-inch rounds onto your baking sheets, approximately 1-inch apart. Continue until you have used all the dough. Bake in the oven, switching positions of your sheets half way through, until the gougères are puffed, golden, and crisp, about 30 minutes. Serve warm
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