In a large bowl, stir together breadcrumbs and milk; let stand to absorb.
Heat oil in a large saucepan over medium heat, then cook onion with ¼ tsp salt until softened, about 7 minutes. Add garlic and cook until fragrant, about a minute more. Cool for a few minutes, then scrape into breadcrumb mixture.
Stir mayo into the breadcrumb mixture, along with parsley, remaining salt, pepper, and cayenne.
When mixture is cool to the touch, stir in the egg then the ground chicken. Use your hands to gently but thoroughly work the mixture together. Using oiled or slightly-dampened hands, form into 6 burger patties. It’ll seem quite soft at this point. Chill the patties for 20 minutes to firm up.
If grilling: Preheat grill to medium-high heat and oil the grates. Grill the patties for about 6-7 minutes per side, or until the internal temperature reaches 165ºF.
If pan-cooking: Heat a tablespoon of oil in a skillet over medium heat. Add the patties and cook for about 6-7 minutes per side, or until the internal temperature reaches 165ºF.
Let burgers rest for a few minutes before serving.
Video
Notes
Tips to keep ground chicken burgers from falling apart:Maintaining the shape of ground chicken burgers can be a bit tricky, but with the right tricks up your sleeve, you'll be all set:Keep Your Hands Wet: If the mixture sticks to your hands while shaping the patties, dampen them with a little water or oil. This not only prevents sticking but also helps to start forming a firm shape from the get-go.Parchment Paper to the Rescue: Lay your carefully crafted patties on parchment paper. If the patties are playing hard to get, cut the paper around them and use this to gently transfer them to the grill or pan. Position them with the parchment side facing up on the cooking surface, then peel off the paper. Smooth sailing!Chill them Before Cooking: Firming up your patties in the fridge before cooking can help them keep their shape while cooking. A short chill session of about 20 minutes in the fridge or 10 minutes in the freezer can work wonders.Flip 'Em Less: The golden rule when your burgers hit the pan or grill: don't be a flip-flopper. Let the burgers cook undisturbed until they lift off easily, signaling that they've set on the bottom and are ready to be flipped. Aim to flip them just once if you can help it.