Preheat the oven at 450°F. Line two baking sheets with parchment paper (or Silpats if you have them).

In a medium saucepan, combine water, butter, salt and sugar, and bring to a boil. Add the flour all at once, reduce the heat to medium, and stir with a wooden spoon for 2 minutes, until mixture forms a ball and moisture has evaporated. (For me, the ball formed much faster than that, but you keep cooking for 2 full minutes anyway.)

Transfer the mixture to a bowl, beat with an electric mixer for 30 seconds at medium speed (you can do it in a stand mixer if you have one, I don't and the hand mixer worked fine.)

Add 4 eggs and continue to mix until completely combined and the batter is smooth and silky.

The batter should form a soft peak with a tip that falls over. (If it's too stiff, beat in the white of the remaining egg, check again, and if necessary, add in the remaining yolk.)

Mix in 3/4 cup of Gruyère and add the pepper.

Thomas Keller of course does this with a pastry bag and pastry tip. I didn't have that, so I just used a cookie scoop to put the small mounds of batter on the baking sheet.  Sprinkle the top of each gougère with the rest of Gruyère.

Place on a lower rack in the oven, and bake for 7-8 minutes, until they puff a bit, then lower heat to 350°F and bake for another 20-25 minutes. When the gougères are done, they should be light golden color. When you break one open, it should be hollow, the inside cooked, but slightly moist (see picture above).

Serve preferably warm.