Position the racks to divide the oven into thirds and preheat it to 425 degrees F. Line two baking sheets with parchment paper or silicone baking mats.

Bring the milk, water, butter and salt to a boil over high heat in a medium saucepan. Make sure that the better has melted. Add the flour all at once, lower the heat and immediately start stirring vigorously with a heavy spoon. The dough will form a ball and there’ll be a light film on the bottom of the pan. Keep stirring for another 2 minutes or so to dry the dough. Dry dough will make puffy puffs.

Transfer the dough into the bowl of a stand mixer fitted with the paddle attachment (or continue to by hand in the pot with a wooden spoon and some elbow grease). Let the dough sit for a minute, then add the eggs one by one, followed by the white, beating until each egg is incorporated before adding the next. The dough may look like it’s separating or falling apart but just keep working. By the time the white goes in, the dough will be cohesive. Beat in the mustard, followed by the cheese and the walnuts. Give the dough a last mix-through by hand.

Scoop or spoon out the dough, using a small cookie scoop. If you’d like larger puffs, shape them with a tablespoon or medium-size cookie scoop. Drop the dough onto baking sheets, spaced about 2 inches apart. (Note that the gougeres dough can frozen on baking sheets at this point.) You can also use a pastry piping bag fitted with a 1/2" tip.

Place the baking sheets in the oven and immediately turn the oven temperature down to 375ºF. Bake for 12 minutes, then rotate the pans from front to back and top to bottom.

Continue baking until the gougeres are puffed, golden and firm enough to pick up, another 15 to 20 minutes.

Serve immediately. They're best served hot from the oven!