Cut potatoes into french fry lengths (a mandoline comes in handy here). Place in a large bowl, cover with cold water, and refrigerate for about 1 hour.
While your potatoes are chilling, heat butter in a 2-qt. saucepan over medium-high heat. Add flour, and cook, stirring until smooth, about 2 minutes. Add shallot and garlic, and cook until soft, about another 2 minutes. Add stock, ketchup, Worcestershire, salt, and pepper, and bring to a boil; cook, stirring occasionally, until thickened, about 10 minutes. Remove from heat and keep warm.
Pour oil to a depth of about 3″ in a Dutch oven, and heat over medium heat until a thermometer reads 325 degrees. Drain potatoes, and dry thoroughly with paper towels. Working in small batches, add potatoes. Fry the potatoes, tossing occasionally, until tender and slightly crisp.
Drain on paper towels, and let cool for 20 minutes. Increase temperature to medium-high, and heat the oil until it reaches 375 degrees. Again work in small batches and return potatoes to oil. Fry potatoes until crisp and golden brown, about 2 minutes. Transfer fries to paper towels to drain briefly and sprinkle them with salt. Set aside and keep warm.
Heat a grill pan over medium high heat. Divide ground beef into two balls and flatten slightly into two hamburger patties. Add both patties to the hot pan. Be sure to sear both sides really well and cook to your preferred doneness – about 5 minutes for medium. As the patties are reaching the end of their cooking time, cut the hamburger rolls in half and butter the insides with the butter. Add the rolls cut side down to the grill pan and toast for a couple minutes.
Now it’s time to build the epic poutine burgers! Add a burger patty to the bottom of each roll. Top with fries, smother the entire thing in gravy, sprinkle on cheese curds, and top with the other half of the roll. You may now stuff your face.