Heat the oven to 350 degrees.
Place a thick mug in the freezer.
Prep the potatoes: Cut the potatoes into 1/4-inch thick sticks. Place into a large bowl and cover completely with cold water for 20 minutes (see note). Drain well and pat dry with a towel. While the potatoes are soaking, make the burger patties.
Mix together the ground beef, steak seasoning, and Worcestershire sauce. Form into even patties. Transfer to a plate, cover with plastic wrap, and reserve in the fridge until you are ready to cook (see note).
Bake the potatoes: Place the potatoes on a parchment lined baking sheet. Cook in the oven until tender, about 15 to 20 minutes. While the potatoes are baking, prep ingredients.
Prep vegetables for cheeseburger per instruction above.
Remove potatoes from the oven and set aside to cool completely.
Prep the root beer float: Pour the cold root beer into the mug inside the freezer, leaving enough room to add the ice cream.
Lightly toast the buns in a toaster oven.
Heat the french fry oil in a pot on medium heat to between 350 to 375°F (177 to 191°C).
Heat a skillet over medium high heat.
Cook the potatoes: Fry them in the oil and cook until crispy and golden brown (cook in batches as needed, overcrowding will result in limp fries). Remove to a paper towel-lined large bowl and season with salt immediately to taste.
Cook the burger patties: add the patties to the heated skillet and cook on both sides, getting a nice crusty char to desired doneness (see note) using a thermometer. When the burger is 3/4 of the way cooked to your liking, add the cheese and cover with a lid to melt.
Compose the burger: Place the patty on the bun with lettuce, tomato, and onion.
Finish the root beer float: Remove from the freezer and carefully scoop ice cream into the mug.
Serve: Enjoy the cheeseburger with french fries, ketchup, pickle, and root beer float.