Make the Sauce: Heat olive oil in a medium saucepan. Add onion, garlic and a sprinkle of salt. Saute on medium until the onion is soft and lightly browned, about 5 minutes.
Pour in the tomatoes along with the oregano, thyme, basil, and salt. Bring to a simmer and let bubble until much of the liquid has been cooked off, about 15 minutes. The sauce will be thick but not dry.
Puree, either in the pot with a stick blend or in a regular blender. Keep the sauce warm while you make the burgers.
Make the Burgers: Mix together the chicken with the parmesan, soy sauce, anchovy, and garlic.
Divide and shape into 4 patties.
Coat them with breadcrumbs: Pour the panko into a bowl and gently press the burgers into the breadcrumbs until fully coated. Set the coated burgers onto a plate.
Fry in a Skillet: Heat 2 tablespoons of olive oil in a large skillet until the oil shimmers and the pan is hot.
Slip the burgers into the hot oil and, cook, turning occasionally until they are cooked and read 155F on an instant thermometer, 12-15 minutes total. Add more oil to the skillet if needed.
Melt the Cheese: Once the burgers are done, top each with mozzarella. Cover the skillet and move it off the heat until the cheese is melted 1-2 minutes.
Toast the Buns: Move an oven rack to the top position and heat the broiler. Brush or spray the buns with a little olive oil and sprinkle with salt. Cook under the broiler until golden brown. (Keep a close eye! They will cook fast.)
Serve: To serve place a burger on a bun and top with some of the tomato sauce. Serve with extra sauce on the side. A little fresh sliced basil on top is a nice touch.