• Cut a small corner from the ground beef packaging and drain off any excess liquid. Transfer to a plate; pat dry with a paper towel. Season with salt and pepper.

Using wet hands, form the ground beef into two [four] ½-inch-thick patties, then coat the patties with the Memphis BBQ rub.

In a large frying pan over medium-high heat, warm 1 to 2 teaspoons oil until hot but not smoking. Add the patties and cook, turning once, until browned but not yet cooked through, 2 to 3 minutes per side. Sprinkle the patties evenly with the cheddar. Carefully add about 1 teaspoon water to the pan, cover, and cook until the cheddar has melted and the burgers are cooked to medium, 1 to 2 minutes. Transfer the burgers to a plate. Wipe out the pan.
While the patties cook, prepare the salad.

• Peel the onion and cut in half crosswise. Thinly slice half the onion [1 onion] into rounds for the burgers; finely chop as much of the remaining onion as you like for the salad.
• Measure ½ cup [1 cup] arugula for the burgers. 
• Coarsely chop the pecans.

In a medium bowl, mix the balsamic vinegar with 1 tablespoon [2 TBL] oil; season to taste with salt and pepper. Add the chopped onion, blueberries, and the remaining arugula and toss to coat. Season to taste with salt and pepper. Sprinkle with the pecans.

In the same pan used for the burgers, place the buns, cut sides down, and cook over medium-high heat until lightly toasted, 1 to 2 minutes. Alternatively, toast them in a toaster oven.

Place the bun bottoms, cut sides up, on a work surface. Top each with a burger, sliced onion, and the reserved arugula. Slather each bun top with as much BBQ glaze as you like. Close with the bun tops.

Transfer the burgers and salad to individual plates. Serve the remaining BBQ glaze on the side.