Classic Hamburger for Two

Preheat grill to medium-high (or see Stovetop Variation).

Combine onion, oil and 1 1/2 teaspoons ketchup in a small saucepan. Cover and cook over medium-high heat, stirring often, until the onion is softened, 4 to 6 minutes. Reduce heat to medium-low, uncover and cook, stirring occasionally, until very soft, 5 to 8 minutes more. Transfer to a medium bowl and let cool for a few minutes.

Meanwhile, combine the remaining 1 1/2 teaspoons ketchup, mayonnaise, relish and vinegar in a small bowl. Set aside.

Add beef, Worcestershire (or steak sauce) and pepper to the onion and gently combine without overmixing. Form into 2 patties, about 3/4 inch thick.

Oil the grill rack (see Tip). Grill the burgers, turning once, until an instant-read thermometer inserted in the center registers 165 degrees F, 4 to 5 minutes per side.

Assemble the burgers on toasted buns with the ketchup-mayonnaise sauce, tomato slices and lettuce.

Stovetop Variation: Coat a nonstick pan, preferably cast-iron (or a grill pan), with cooking spray and heat over medium-high heat for 1 to 2 minutes. Add burgers, reduce heat to medium and cook, turning once, until an instant-read thermometer registers 155 degrees F (for pork and bison) or 165 degrees (for beef or chicken), 4 to 5 minutes per side.