Set a box grater over a few layers of paper towel. Grate the white onion onto the paper towel, then gather the towel and gently squeeze out as much liquid as possible. Transfer the grated onion to a large bowl.

Using the same grater, grate the cold butter directly into the bowl with the onion.

Add the ground chicken, mayonnaise, grated Parmesan, minced garlic, Worcestershire sauce, Dijon mustard, lemon zest, kosher salt, and black pepper to the bowl. Mix gently with your hands 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 into the center of each patty with your thumb to help them cook evenly.

Place the patties in the freezer 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).

Place the chilled patties directly over the heat, close the lid, and cook for 5 to 6 minutes per side. Use an instant-read thermometer to check for an internal temperature of 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, butter the cut sides of the buns. Place them butter-side down on the grill grates 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, the grilled chicken patty, more dressing, a few slices of red onion, an extra lettuce leaf, a sprinkle of shaved Parmesan, and a handful of crushed croutons. Cap with the top bun.

Serve immediately with your favorite side dishes, such as sweet potato fries or a simple green salad.