First, pickle the red onion by bringing a cup of water and the first 3 ingredients to a boil in a saucepan and pouring over the onion in a small bowl. Steep for about 20 minutes, drain, and cool.
Preheat oven to 425 degrees. Toss the cauliflower, sweet potato, and beets with olive oil and season with salt and pepper. Place in a large, shallow pan and bake until soft but not mushy, about 20 to 30 minutes. Let cool, then refrigerate.
Just before serving, toss the pickled onion, roasted vegetables, olives, and oregano with Yogurt Dressing (you will have dressing left over).
To serve, arrange a few lettuce leaves on each salad plate, top with vegetable mix, spoon on more dressing if desired, and sprinkle with feta.