Cut the potatoes into 1/4-inch thick sticks. Place into a large bowl and cover completely with cold water for 20 minutes.
For the patty melt: Add the oil and onions to a saucepan on medium heat; cover with a lid. Let the onions cook, stirring occasionally until they become soft and golden brown (if the onions get too dark add a tablespoon or two of water; this will smooth out the coloring). Remove from the pan and set aside. Use the same pan to cook the burgers.
Drain the potatoes well and pat dry with a towel.
Blanch the fries: If using the oven, heat the oven to 350 °F (177 °C). Place fries on a parchment-lined baking sheet. Cook in the oven until tender, about 15 to 20 minutes.
If using oil: heat the oil to 300 °F (150 °C) in a dutch oven or deep fryer. Fry fries in small batches until softened, about 6 to 10 minutes.
Once the fries are soft, set them aside to cool completely.
Mix together the ground beef, steak seasoning, and Worcestershire sauce and form oblong patties to fit the shape of the bread.
In a skillet on medium heat, cook the burgers on both sides to your desired doneness (see below) using a thermometer. Then remove and set aside.
Mix together the ketchup and mayo in a bowl. Season with salt and pepper to taste.
Layer the bread with cheese, onion, and burger.
Grease the skillet with nonstick spray and place over medium-low heat. Cook the sandwich on both sides until the bread is golden brown and the cheese is melted.
Fry the fries: Heat the oil to 375 °F (190 °C) in a dutch oven or deep fryer (or increase the heat if you blanched the fries in oil). Add the cooled fries to the oil in small batches and cook until crispy and golden brown (overcrowding the oil will result in limp fries). Remove to a paper towel-lined large bowl and season with salt immediately to taste.
Cut the patty melt in half; serve with sauce, french fries, ketchup, pickle, and sparkling water.