Combine 2 tablespoons olive oil, shallot, garlic, vinegar, 1/4 teaspoon of the salt, sugar, pinch each of dried thyme and oregano, and a few shakes of black pepper in a shallow bowl. Whisk to blend, and set aside.
Set a ridged grill pan over medium heat, and brush it lightly with olive oil. Place the zucchini slices on the hot surface in a single layer, and cook on both sides until just tender and decorated with golden grill marks. Transfer the cooked zucchini directly to the marinade. You might need to do this in a couple of shifts.
Let the zucchini rest in the marinade to absorb the flavors - about a minimum of 30 minutes. Longer is also fine.
Combine the Parmesan with pinches of dried thyme and oregano in a small bowl. Line a toaster oven tray with foil, and brush it lightly with olive oil. Place the walnut halves on the tray, with their more concave sides facing up. With a tiny spoon (if you have one) sprinkle the walnuts lightly with the cheese-herb mixture. There should be enough of it to just cover 20 walnut halves. Place the tray in the toaster oven on the broil setting, and leave it in there until the cheese melts slightly and the tops are light golden. This will only take a minute or two. Watch carefully so it doesnt burn! Remove from the oven and cool.
Serve the zucchini at room temperature or cold, topped with the walnuts, and a scattering of any or all of the Optional Extras.