In a bowl, whisk flour and salt together; set aside.
In a saucepan over medium heat, add shortening and water; bring to a boil.
When melted, add flour and stir vigorously until it releases from the sides of the pot and forms a ball, about 2 minutes.
Transfer to the bowl of a stand mixer. Using the paddle attachment, beat the dough on medium-high speed for 1 minute. Let it cool for 3 minutes.
Preheat oven to 425ºF and line two large baking sheets with parchment paper; set aside.
On medium speed, add 1 egg at a time and mix well between each addition. Add the egg white and process for 30 seconds.
Add Dijon, cheese, thyme, rosemary and pepper. Mix until combined, cleaning the sides and the bottom of the bowl.
Using a portion scoop of about 1 tablespoon, measure the dough out and drop it onto the prepared baking sheet, leaving 2 inches between each.
At this point, the dough can be refrigerated or frozen otherwise, brush the egg wash on each dough ball.
Transfer to the preheated oven and bake for 3 minutes.
Reduce heat to 350ºF and bake for 30 to 35 minutes or until puffed and golden - DO NOT OPEN THE OVEN DOOR under any circumstances! If the dough is frozen, leave them in the oven for an extra 8 to 10 minutes.
Remove from the heat and serve immediately. Makes 36 gougères.