For the bacon onion magic: Heat a large saute pan over medium heat. Add the oil and bacon and cook until the fat has rendered and the bacon is crisp, about 8 minutes.
Remove the cooked bacon with a slotted spoon and set aside on a paper towel-lined plate, reserving 2 tablespoons of the bacon fat in the skillet. Reserve the remaining bacon fat for another use, if desired.
Add the butter to the bacon fat in the saute pan and melt over medium heat. Add the onions and cook over medium-low heat, stirring occasionally, until softened and lightly caramelized, about 15 minutes. Stir in the cooked bacon, then add the vinegar, sugar, thyme, salt and pepper and continue to cook over medium-low heat until the sauce has thickened and has a jam-like consistency, about 10 minutes. Remove from the heat and set aside.
For the diner-style burger sauce: Combine the ketchup, mustard and onions in a small bowl or airtight container until ready to use.
For the diner-style double burger: Heat a double-burner griddle over medium-high heat for at least 10 minutes. Season the griddle with the oil to prevent sticking.
Meanwhile, loosely form the meat into eight 2-ounce balls and set aside.
Put the balls of meat on the griddle and smash them very flat with a large heavy-bottomed metal spatula. Season with salt and pepper and top each smashed patty with 1/2 tablespoon Bacon Onion Magic. Cook, undisturbed, until well browned, about 1 minute. Flip the patties and top each one with 1 cheese slice. Cook until the cheese is melted around the edges and the bottom of each burger is browned, about 2 minutes.
Meanwhile, on each potato roll bottom, spread 1/2 tablespoon Diner-Style Burger Sauce and top with 6 pickle slices. Make double patties on the griddle pan by stacking 4 of patties with the remaining 4 patties cheese-side up. Transfer the double patties to rest on top of the pickle slices. Spread 1/2 tablespoon Diner-Style Burger Sauce on each of the bun tops, then serve.
The Bacon Onion Magic can be made ahead, cooled and stored in an airtight container, too.