Technically, these puffs are called gougère which in French cooking is a baked savory choux pastry made of choux dough (the same kind used for cream puffs) mixed with cheese.
Preheat oven to 375 degrees.
In a large heavy saucepan over medium heat, cook the water, butter, and salt. Bring to a simmer and cook until the butter melts, stirring to combine. Then add flour all at once and cook, stirring vigorously with a wooden spoon. The mixture should start to come together and pull away from the side of the pan after about 2 minutes. Remove from heat and cool slightly, about 3 minutes.
One at a time, add 4 eggs, beating well after each addition. The batter will separate at first but will become smooth as each egg is mixed in. The mixture should be glossy and just stiff enough to hold soft peaks. If batter is too stiff, beat remaining egg in a small bowl and add to batter 1 teaspoon at a time, beating and then testing batter until it reaches proper consistency. Stir in cheese and dill.
Line 2 large baking sheets with parchment paper. Using a 1 to 1 1/2 inch diameter scoop, drop the batter by scoopfuls onto the prepared baking sheets, spacing the mounds about 1 inch apart. Bake until the cheddar puffs are golden brown, crisp when tapped, and are puffed up, 25 to 30 minutes. Be sure to switch the baking sheets between the oven racks and rotate them 180 degrees halfway through baking to promote even baking. Serve warm.
SIDE NOTE - Puffs can be made ahead of time, cooled completely, and then sealed in plastic bags. Puffs can be refrigerated for 2 days or frozen for 1 week. To reheat, place puffs on baking sheets in a preheated 350°F oven for 7-10 minutes if chilled or 15 minutes if frozen or until heated through.
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