Place the turkey in a large mixing bowl. Add the onion, mayonnaise, and Worcestershire sauce. Very gently blend the turkey with the other ingredients until well combined. Be careful not to squish or squeeze the turkey, which can result in less tender burgers. Divide the meat into 4 equal portions.
Form each portion into a patty, working as lightly as possible with the meat, not squishing it. Use your thumb to make a deep depression in the center of the patty, about 1 inch in diameter, and halfway through the thickness of the patty. Season both sides of the burgers with salt and pepper.
Heat a gas grill to high, or heat the coals in a charcoal grill until they are glowing a bright orange with ash all over the outside of the coals. Lightly brush both sides of each patty with the oil. Grill the burgers for 5 minutes on each side until just cooked through (an internal temperature of 165 degrees). Add the cheese, if using, during the last minute of cooking. Close the top of the grill while the cheese melts.
Place the split buns, cut sides down on the hot grill grates for just about 10 seconds, then remove them. Place the burgers on the bottom halves of the buns, top as desired, and place the top of the buns on the burgers.
Notes
Turkey Burger Tips
Keep the meat in the fridge until you are ready to shape the patties, and keep the patties in the fridge until you are ready to grill them. This prevents bacteria from forming.
Be careful not to squish or squeeze the turkey, which can result in less tender burgers.
Do not press down on the burgers as they cook! You will simply be pressing all of those flavorful juices out of the burger, into the fire. You want those juices where they belong, right there in the meat. (Pressing down on the burger can also cause flare-ups, which are annoying and possibly dangerous.)
Don’t flip the burgers constantly. Leaving them sit for a few minutes will give them those nice grill marks and prevent them from falling apart when you turn them.
Never put cooked burgers on the plate you used to bring the uncooked patties to the grill. This can cause contamination, so use a fresh plate, platter, or board for your cooked patties.
Set your gas grill to high for grilling burgers, and for a charcoal grill, make sure your coals are bright orange and ashy. You want high heat here.
Make sure to cook them through to a safe internal temperature of 165 degrees.
If grilling outdoors isn't an option, you can also cook these burgers in the oven or in a pan on the stove. A grill pan is great, but you can also use a heavy skillet, like a cast-iron pan. Preheat the pan before adding the burgers; the cooking times should be similar.
Leftover burgers can be stored in an airtight container for up to 3 days in the fridge. Reheat in the microwave before serving, or warm on the grill.