In a large bowl, gently mix together the gound beef, onions, thyme, pepper, rosemary, coriander, fennel, cayenne, egg, and oil, if usiing. Season with salt. Divide the meat into 4 portions; shape them into 1"-thick patties. Wrap patties in plastic wrap; refrigerate until cold. This will help to firm them up, as they're moister than most burgers owing to the addition of the oil and the egg.
Prepare a medium-hot charcoal fire or heat a gas grill to medium-high (or heat a tablespoon of canola oil in a large cast-iron skillet over medium-high heat). Cook burgers, flipping once, until cooked to desired doneness, about 12 minutes total for medium rare. Serve on buns. Enjoy!