Place a box grater over a few layers of paper towels. Grate the onion directly onto the paper towels, then use the towels to squeeze out as much liquid as possible. Set aside in a small bowl.

Using the same grater, grate the cold butter onto a plate and place it in the freezer while you mix the burgers.

In a large bowl, combine the grated onion, grated butter, ground chicken, mayonnaise, Parmesan, garlic, Worcestershire sauce, Dijon, lemon zest, salt, and pepper. Mix gently until just combined—do not overwork.

Line a small baking sheet or plate with parchment paper. Divide the mixture into 4 equal portions and shape each into a patty about 1/2 to 3/4 inch thick. Press a shallow indent in the center of each patty with your thumb.

Place the patties on the prepared sheet and freeze for 20 minutes. This firms them up so they hold their shape on the grill.

Clean the grill grates and preheat your grill to medium-high heat (about 400°F to 450°F).

Place the frozen patties directly over the heat. Close the lid and cook for 5 to 6 minutes per side, or until an instant-read thermometer inserted into the center registers 165°F.

During the last 1 to 2 minutes of cooking, top each patty with a slice of provolone cheese and close the lid to melt.

Remove the burgers from the grill and let them rest for 5 minutes.

While the burgers rest, spread the cut sides of the buns with softened butter. Place them butter-side down on the grill and cook for 30 to 60 seconds, until lightly toasted with grill marks. Remove carefully.

On each bottom bun, layer a lettuce leaf, a drizzle of Caesar dressing, a chicken patty, another drizzle of dressing, a few slices of red onion, more lettuce, a sprinkle of shaved Parmesan, crushed croutons, and the top bun.

Serve the burgers immediately with your favorite sides, such as sweet potato fries or a simple green salad.