Place the ground chicken in a large mixing bowl. Add the remaining burger ingredients, and use your hands, a silicone spatula, or a metal spoon to thoroughly mix.
Once completely combined, use a ½-cup measuring cup to scoop a heaping portion of the mixture, then use your hands to form a plump and compact burger patty. This makes 8–9 patties that weigh about 4.5–5 ounces (127–142g) each.
Place the patties onto a parchment paper-lined baking sheet or plate. Cover and refrigerate for at least 30 minutes and up to 6 hours. This ensures the patties will hold their shape. You can also freeze the patties for up to 3 months. Thaw in the refrigerator.
Clean the grill and grease with vegetable oil. Pour a little vegetable oil on a paper towel and carefully rub all over the grates. Preheat grill to high. Place cold chicken burgers on heated grill and cook for 5 minutes with the lid closed. Flip burgers over and cook, covered, until a meat thermometer registers 165°F (74°C) when inserted into the center of the burger, about 4 more minutes. Overcooking will quickly dry them out, so keep a close eye.
Spread pesto on the inside of each bun half, then layer chicken burger, a slice of mozzarella, basil leaves, and a slice of tomato in between the bun halves.
Store leftover chicken burgers in an airtight container in the refrigerator for up to 5 days.
