Preheat oven to 450 degrees. Halve the onion horizontally (not through the roots). Peel and finely dice half the onion. Peel and slice the other half into 1/2-inch rings. Separate the rings and very finely mince the innermost rings. Thinly slice the tomato.

Make the secret sauce: in a small bowl, mix together the mayonnaise, minced onion (from the innermost rings), and 1/2 teaspoon smoked paprika. Season with salt and pepper.

Make the onion ring batter: in a medium bowl, whisk together the flour and 1/2 cup water. Season batter with salt and pepper. Place the panko in another medium bowl and season generously with salt and pepper.

Heat a drizzle of oil in a large pan over medium heat. Add the diced onion to the pan and cook, stirring occasionally, until soft and slightly caramelized, 8-10 minutes. Stir in 1 tablespoon dijon mustard and season with salt and pepper. Set onion mixture aside and wash out the pan.

Meanwhile, form the ground beef into 4 equal balls. Flatten each ball into a 1/2-inch patty, about 4-5 inches in diameter. Season each patty with salt and pepper.

Make the onion rings: working one at a time, coat the onion rings first in the batter, and then in the panko, pressing to adhere. Place coated onion rings onto a lightly oiled baking sheet. Once all onion rings are coated, place baking sheet in the oven for about 10 minutes, turning onion rings over halfway through cooking, until golden brown. HINT: Keep an eye on these, they can burn quickly!

While the onion rings bake, cook the burgers. Heat a drizzle of oil in the same pan you cooked the onions in over high heat. Once hot, add the burger patties (working in 2 batches, if necessary) and cook about 2 minutes per side, until browned and almost cooked to desired doneness. Top two patties with cheddar cheese and cook another minute, until melted.

Remove the onion rings from the oven to cool for 2-3 minutes. Halve the buns and place in the buns in the oven to toast for 2-3 minutes.

Assemble the burgers: place two patties onto each bun (one with cheese, one without) and top with the dijon-caramelized onions, tomatoes, and lettuce. Spread the top bun with 1 tablespoon secret sauce. Serve cheeseburgers alongside the onion rings and enjoy!