Preheat the broiler. Put the poblano on a baking sheet and broil, turning, until charred in spots, about 8 minutes. Transfer to a plate and let cool. Reduce the oven temperature and bake the onion rings as the label directs. Season with salt, pepper and 1/4 teaspoon each chili powder and cumin.
Meanwhile, combine the ketchup, cilantro, a pinch of lime zest and half of the lime juice in a small bowl; add more lime juice and salt and pepper to taste. Refrigerate until ready to use.
Mix the ground beef, 1/2 teaspoon lime zest and the remaining 1 3/4 teaspoons chili powder and 3/4 teaspoon cumin in a large bowl with your hands until just combined. Form into four 3/4-inch-thick patties; season both sides with salt and pepper. Heat the vegetable oil in a large nonstick skillet over medium-high heat. Add the burgers and cook until browned, 2 to 3 minutes per side for medium rare.
Peel, stem and seed the broiled poblano; cut into strips. Place the burgers on the buns with the ketchup sauce, lettuce and poblano. Serve with the onion rings and the remaining ketchup sauce.