This recipe seems simple in nature, but when you look closer you’ll see there are extra steps taken to make sure that a classic such as a Cheddar cheeseburger is treated well and tastes good. Tender shallots are cooked down and braised in white-wine vinegar to create a topping to a tender patty mixed with minced garlic. A little bit of mayonnaise and peppery arugula are all that are needed to complete this unassuming yet delicious burger.
Heat a nonstick skillet over medium-low heat. Add 2 teaspoons oil and swirl to coat. Add shallots and ¼ teaspoon salt and cook for 15 minutes or until golden brown, stirring occasionally. Stir in vinegar and cook 1 minute. Remove from heat and keep warm.
Gently combine the garlic and beef. Divide the meat mixture into 4 equal portions, gently shaping each into a ½-inch-thick patty. Press thumb in the center of each patty, leaving a nickel-sized indentation. Sprinkle evenly with ¼ teaspoon of salt.
Heat a large cast-iron skillet over medium-high heat. Add 1 teaspoon oil to pan and swirl to coat. Add the patties, and cook 3 minutes on each side or until desired degree of doneness. Top each patty with 2 tablespoons the cheese, cover, and cook 1 minute or until cheese melts.
Place ¼ cup arugula on the bottom ½ of each bun and top with 1 patty and ¼ of the shallot mixture. Spread about 2 teaspoons mayonnaise on the cut side of the top ½ of each bun and place on top of burgers.