In a food processor, pulse the greens until very finely chopped.
In a mixing bowl, combine the greens and the meat. Add the onion and its juice and the Worcestershire; season with salt and pepper. Form into 4 patties, thinner in the centers for even cooking. Rinse out the processor bowl and return it to the base.
Heat a cast-iron skillet over medium-high. Add the oil, one turn of the pan. Add the patties and cook, turning occasionally, until browned, about 8 minutes. During the last minute or so of cooking, top each patty with 1 slice of cheese; tent loosely with foil to melt the cheese.
In the processor, combine the avocado, sour cream, herbs, lemon juice, garlic and hot sauce. Season with salt and process into a smooth, thick dressing.
Serve the patties on the rolls with the lettuce, tomato, onion and lots of dressing.