For the mayonnaise: To a bowl, add the mayonnaise, mustards, hot sauce, cornichons, green onions, parsley and some salt and pepper. Stir to combine. Taste and adjust seasoning if needed. Cover and refrigerate until ready to serve.
For the burgers: Stir together the paprika, salt, pepper, thyme, cayenne, garlic powder and onion powder in a small bowl.
Mold the meat into patties. Brush with oil and sprinkle both sides with salt. Sprinkle 1 side of each patty with the spice mixture, making sure to rub the spices into the meat, and then drizzle with oil before grilling.
Preheat a griddle pan to medium heat.
Add the canola to the pan just prior to cooking. Place the burgers on the pan and cook until slightly charred and the spices have formed a crust, about 1 1/2 minutes (be careful not to burn the spices). Flip the burger over, lower the heat to medium and continue cooking to desired doneness. Top each burger with 2 slices of cheese during the last 30 seconds of cooking, until the cheese is melted.
Put the burgers on the buns, top with the ham, some of the onions, some of the mayonnaise sauce and some potato chips. Use a skewer to hold the burger together.