In a medium bowl, combine the ground turkey, parsley, grill seasoning, mustard and poultry seasoning. Form 4 patties; using your thumb, make an indentation in the center of each to prevent bulging while cooking.
In a large nonstick skillet, heat the EVOO, 1 turn of the pan, over medium-high heat. Add the patties and cook until the juices run clear, 6 to 7 minutes on each side. During the last few minutes of cooking, top each burger with a cheddar slice, tenting loosely with foil to melt the cheese.
Meanwhile, in a small bowl, combine the zucchini, bell pepper, red onion, thyme, hot sauce and lime juice. Season with salt.
Toast and butter the English muffins. Set a lettuce leaf and burger on each muffin bottom and top with some zucchini relish and a muffin top.