In a small, heavy-bottomed skillet, add the walnuts over medium heat. Cook, stirring or shaking the pan occasionally, until lightly toasted, 2 to 4 minutes. Pour into a bowl and set aside.
Position racks in the top and bottom thirds of the oven and preheat to 425°. Line two baking sheets with parchment paper or silicone baking mats.
In a medium saucepan, add the milk, water, butter, and salt; bring to a rapid boil over high heat. Add the flour all at once, lower the heat and stir rapidly with a heavy spoon or whisk. The dough will form a ball and there will be a light film on the bottom of the pan. Keep stirring to dry the dough slightly, 1 to 2 minutes more.
Turn the dough into the bowl of a stand mixer fitted with the paddle attachment, or a medium mixing bowl. Let the dough sit for a minute, then add the eggs one by one, beating with the mixer or a wooden spoon until each egg is incorporated before adding the next. (The dough may look as though it’s separating or falling apart – just keep working; it will come together by the time the last egg goes in.) Beat in the mustard followed by the cheeses and the chopped pecans.
Using a small (1 ½ teaspoon) cookie scoop or spoon, scoop the dough onto the prepared baking sheets, leaving about 2 inches between each.
Transfer to the oven and immediately turn down the temperature to 375°F. Bake for 12 minutes, then rotate the pans from front to back and top to bottom. Continue baking until the gougères are puffed, golden and firm enough to pick up, 15-20 minutes more. Remove and serve immediately.