Preheat grill to medium-high (or rely on Stovetop Variation).
Combine onion, oil and 1 tablespoon ketchup in a medium saucepan. Quilt and cook over medium-high heat, stirring on the final, till the onion is softened, 5 to 7 minutes. Sever heat to medium-low, bid and cook, stirring every infrequently, till very soft, 5 to eight minutes extra. Transfer to a medium bowl and let frosty for a jiffy.
In the period in-between, mix the final 1 tablespoon ketchup, mayonnaise, be pleased and vinegar in a limited bowl. Advise apart.
Add crimson meat, Worcestershire (or steak sauce) and pepper to the onion and gently mix without overmixing. Make into 4 patties, about 3/4 journey thick.
Oil the grill rack (rely on Tip). Grill the burgers, turning as soon as, till an instant-read thermometer inserted within the guts 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.
Way Forward Tip: Put collectively ketchup-mayonnaise sauce (Step 3) and refrigerate for as much as 1 day.
Coat a nonstick pan, ideally cast-iron (or a grill pan), with cooking spray and warmth over medium-high heat for 1 to 2 minutes. Add burgers, within the low cost of heat to medium and cook, turning as soon as, till an instant-read thermometer registers 155°F (for pork and bison) or 165° (for crimson meat or hen), 4 to 5 minutes per side.
Tip: To grease a grill rack, oil a folded paper towel, abet it with tongs and rub it over the rack. (Attain now now not exercise cooking spray on a scorching grill.)