1. Preheat oven to 400 degrees. Heat wine, 1/2 cup water, butter, sugar, and 3/4 teaspoon salt in a medium saucepan over medium-high heat until butter melts. Remove from heat and immediately stir in flour using a wooden spoon. Cook over medium heat, stirring constantly, until mixture pulls away from sides of pan and a film forms on the bottom, about 3 minutes.

2. Transfer dough to the bowl of a mixer and beat on medium speed until slightly cooled, about 1 minute. Beat in eggs, 1 at a time, then cheddar and blue cheeses.

3. Spoon 26 mounds of dough (about 1 1/2 inches wide) onto 2 parchment-lined baking sheets. Brush with egg wash and sprinkle with Gruyere. Bake for 10 minutes. Reduce oven temperature to 350 degrees and continue to bake until gougeres are browned and cooked through, about 20 minutes more. Serve warm or at room temperature.