For the spicy mayonnaise: Whisk together the mayonnaise and pickle juice in a small bowl. Add the sriracha, a little at a time, adding more to your taste.
For the pickle mix: Stir together the chopped pickles and grainy mustard. Set aside.
For the burgers: Put the meat in a large bowl and spread it all over the bottom and a little up the sides. This will help distribute the seasoning evenly throughout the meat. Sprinkle liberally with salt and pepper. Stir in the mayonnaise.
Test the seasoning by taking a tiny piece of the meat mixture and forming it into a patty. Set a small skillet over medium heat, add a touch of oil and sear the patty on each side. Let cool slightly and taste. If it needs more salt and pepper, add it to the raw mixture. Repeat the test as needed.
Divide the meat into 8 equal patties (3 ounces each) and roll each into a ball. Place the balls on a clean surface and use the palm of your hand to gently flatten to 3/4-inch thick and 2 to 3 inches in diameter. Alternatively, use a round cookie cutter to mold the burgers into uniform "rounds" by pressing the meat into the mold and making the burgers one by one. Make an indent in the middle of each patty (as the meat cooks the center of the patty will puff up; this will keep the thickness even).
Preheat the oven to 375 degrees F.
Heat a large cast-iron skillet over high heat and add just enough canola oil to coat the bottom. When the oil begins to smoke lightly, add the burgers in a single layer with space in between each, cooking in batches if needed. Press the patties down with a metal spatula so they are fairly thin and cook, undisturbed, until the edges brown, 2 to 3 minutes. Flip using a metal spatula and place a slice of cheese on top of each to melt as the burgers finish cooking. Cook to desired doneness, 3 to 5 minutes longer.
Place the bun halves on a baking sheet and toast in the oven until light brown, 3 to 5 minutes. Place a dollop of spicy mayonnaise on the bottom halves but don't spread it around. Top with the hamburgers followed by pickle mix, more spicy mayo, and another hamburger. Finish with more pickle mix, spicy mayo and the top buns. Serve immediately.
Recipe courtesy of Alex Guarnaschelli