In a mixing bowl, whisk together the ketchup, hot sauce, Worcestershire, paprika, horseradish, onion, pickle, pickle juice and mustard. Fold in the pastrami, Swiss and mascarpone. Chill until ready to use.
Set yourself up a small bowl of cold water. Working with 2 to 4 wonton wrappers at a time, put 1 tablespoon of the filling onto the center of each wrapper. Dip your finger in the water and moisten all the edges of the wrapper. Bring up the 2 opposite corners then the other 2 opposite corners, pinching together in the center and sealing all 4 seams. You will end up with a four-sided pyramid. Place on a parchment-lined-sheet tray while you assemble the rest. Continue to make wontons until you've used all of your filling.
Pour enough oil to fill a Dutch oven about a third of the way. Heat over medium heat until a deep-fry thermometer inserted in the oil reaches 375 degrees F. (If you don't have a thermometer, a cube of bread will brown in about 3 minutes.)
Add 4 to 6 wontons at a time to the preheated oil and fry until golden brown and crunchy, 2 to 3 minutes. Remove to a paper towel-lined sheet tray and lightly season with salt. Repeat with the remaining wontons. Serve immediately with more mustard!
Once the wontons are made, they can be kept in the freezer for up to a month. When ready to cook, fry from frozen.