Preheat oven to 425F.
Start the taters: Combine Parmigiano, salt, rosemary, hot pepper flakes and grill seasoning in a bowl. Pour four portions of taters onto a non-stick cookie sheet. Bake until almost crisp (about halfway through the cooking time on the package), then remove and sprinkle them with a handful of the cheese, tossing them a little to make sure they're coated, and then finish baking them off. Sprinkle them with cheese and herb mixture, tossing them around a bit so the mixture sticks. As the frost starts to melt, the flavorings will set into place.
Make the dipping sauce: Heat EVOO in a small saucepan over medium-high heat. Add grated onion (onion can be grated right over the pot) and garlic, and cook 1-2 minutes. Add tomatoes, reduce heat to medium and cook, stirring frequently, for 10-12 minutes. Remove from heat and reserve.
While the sauce is working, prepare the burgers: In a bowl, combine the chicken, finely chopped garlic, anchovies, a handful of cheese, a pinch of salt and a generous amount of pepper, Worcestershire, parsley and lemon zest. Mix the meat and form 4 oval-shaped, rather than round, burger patties.
Heat a large nonstick skillet with 1 tablespoon of EVOO, a turn of the pan, over medium-high heat. When hot, add the chicken patties and cook for 3-4 minutes on each side.
Preheat the broiler and toast the bread on a cookie sheet or broiler pan. Once lightly golden in color, remove from oven and rub the breads with cracked garlic. Drizzle bread with the EVOO.
Combine Dijon, lemon juice and 2-3 tablespoons of EVOO with salt and pepper, and toss the greens with it.
Place the patties on the bun bottoms and top them with a pile of romaine, sliced tomatoes and bun tops. Serve the burgers with the Parmigiano taters and a bowl with the dipping sauce alongside.