In a large mixing bowl, combine the ground chuck with kosher salt, cracked black pepper, onion powder, minced garlic, fresh oregano, chopped red onion, tomato paste, balsamic glaze, and panko bread crumbs. Mix gently using your hands until well incorporated, being careful not to overwork the meat.

Divide the mixture into four equal portions and shape them into patties roughly ¾ inch thick. Press a thumbprint into the center of each patty to help prevent them from puffing up while cooking. Refrigerate for about 20 minutes.

Preheat your grill to high heat, about 450°F to 500°F. To prevent sticking, oil the grates using a paper towel dipped in vegetable oil.

Once the grill is hot, carefully place the patties on the grates. Cook for about 4 minutes on one side without moving them. Flip the patties and continue grilling for another 4 minutes, monitoring the internal temperature.

Prepare your buns by placing them cut-side down on the grill for about 1 minute to lightly toast. Layer each bun with a grilled patty, fresh mozzarella, tomato slices, and basil leaves. Drizzle with balsamic glaze.

Whisk together mayonnaise and basil pesto in a small bowl until well blended. Spread a generous amount of pesto mayo on the inside of each toasted bun before placing the patties on top.