Add red onion to a small glass bowl and barely cover with a mixture of equal parts water and red wine vinegar. Set aside.
In another small non-reactive bowl, combine vinegar, oregano, basil, garlic, red onion, and mustard. Slowly whisk in olive oil until the mixture is emulsified. Season with salt and pepper, to taste. Set aside.
Add prepared Romaine lettuce to a large serving bowl. Starting in the center, add the feta cheese to form a row. On each side of the feta, add a row of chopped black olives. Then add two rows of sliced grape tomatoes on the other side of the black olives. Finish by filling in the far end with the sliced cucumbers.
Once all ingredients are in place, drain the red onions and gently pat dry. Then carefully arrange them in a thin row on either side of the feta cheese. You want to wait until the end to add the onion to give them time to soak and to prevent them from falling down between the larger toppings and getting lost.
If desired, sprinkle the top with additional dried oregano and serve immediately with Greek Dressing - or cover and place in the refrigerator for up to one day before serving.