Preheat oven to 400°F. Line a baking sheet with foil or parchment paper and lightly grease with cooking spray. Spread out the frozen fries in a single layer and bake them according to the package directions until golden brown and crispy.
To make the gravy, set a medium saucepan over moderate heat with the butter. Once melted, add in the shallot and garlic and cook until softened, about 3 to 5 minutes. Stir in the flour and cook for about 30 seconds. Whisk in the beef stock and bring up to a simmer. Cook until just beginning to thicken and then stir in the vinegar, Worcestershire sauce, ketchup, salt and pepper. Reduce flame to low and cook until reduced slightly and thick, about 20 minutes.
To make the burgers, place the ground beef in a large bowl. Season with salt, pepper and Worcestershire sauce. Using a box grater, grate the very cold stick of butter into the bowl with the beef. Use your hands to gently mix it all together. Then divide the mixture into four equal parts and shape each into a thick burger patty. Chill for about 15 minutes.
Set a large skillet over medium high heat with the remaining 2 tablespoons butter. Once melted, add in two burger patties and cook until golden brown on the first side, about 4 to 5 minutes. Flip over and then using a spoon, baste the patties with the butter from the pan. Continue cooking and basting for another 3 to 4 minutes. If you prefer the grill, fire it up and repeat the same steps until patties are beautifully browned. Transfer to a platter and cover loosely with a piece of foil to keep them warm. Repeat with the remaining two patties.
To assemble, place a burger on top of each bottom bun. Pile a handful of fries on top of each burger and top with cheese curds. Spoon the gravy over the fries and garnish with fresh thyme. Place the top buns on each and serve immediately.