Preheat oven to 375° F. Line a large rimmed baking sheet with parchment paper.

Place wine, water, butter, salt and pepper in a heavy-bottomed medium saucepan. Bring to boil over medium heat, stir until butter is melted. Stir in flour; reduce heat to medium-low. Stir vigorously about 1 minute, until mixture forms large dough clumps and a film forms on bottom of saucepan. Remove from heat; cool about 5 minutes.

Meanwhile, whisk eggs in a medium bowl. Transfer 1 tablespoon beaten egg to a small bowl and reserve. Add C of remaining beaten eggs to the saucepan; whisk until well incorporated into the dough. Add remaining eggs in 2 additions, stirring each time until eggs are completely absorbed. The dough will be sticky. Mix in blue cheese until just blended.

Drop dough by teaspoon onto baking sheet, forming about 24 walnut-size mounds and spacing about 1 inch apart. Using pastry brush, brush each mound with reserved egg, smoothing the tops slightly. Bake gougeres until puffed, golden brown and dry, about 30 minutes.