- Preheat oven to 375°F.
- Line 2 baking sheets with parchment paper, and set sheets aside.
- Place butter, ¼ cup milk, water, ¼ teaspoon salt and pepper in 2-quart saucepan, and heat over medium heat.
- Bring to a boil, remove from heat, and add flour and baking powder.
- Stir well with wooden spoon, and return to heat.
- Cook until dough pulls away from sides of pan and forms ball.
- Transfer dough to bowl of electric mixer fitted with paddle attachment, and, setting mixer on low, mix until dough is just warm, about 2 minutes.
- Add eggs, 1 at a time, and add ½ cup cheese.
- Beat mixture until uniformly smooth and shiny, about 12 minutes.
- Place dough into pastry bag fitted with #3 tip.
- Pipe gougères into small mounds on baking sheets, about 1 inch round.
- Space evenly about ½ inch apart, making about 18 gougères per sheet.
- Brush tops with remaining 2 tablespoons milk, and sprinkle with remaining cheese and salt.
- Bake 20 to 25 minutes, or until gougères turn golden brown.
- Remove from oven, and serve warm.