In a large heavy-bottomed pot, combine the brown sugar, molasses, cinnamon, ginger, cloves and white pepper. Bring to a full boil over medium-high heat; remove from heat and immediately add the baking soda and stir well. (The mixture will foam up...just keep stirring!)
Add the butter a couple of chunks at a time, stirring to combine between each addition. Once all of the better has been added and has melted, stir in the applesauce.
At the point, the mixture should still be warm but not hot. Add the egg and stir. Finally, add the salt, then the flour. Stir until the dough comes together - the dough should be very soft and still slightly warm.
Roll out on a well-floured surface. Cut with cookie cutters or use a large glass to make round cookies. Place on a parchment-lined baking sheet and bake for 12 minutes.