Place oven racks in top and lower thirds of oven. Preheat oven to 425°F. Line 2 large baking sheets with parchment paper.
Add potatoes to large pot of salted water. Cover with lid slightly ajar and bring to boil. Cook potatoes until fork-tender, about 8 to 12 minutes. Drain.
Divide potatoes and cauliflower between prepared pans; drizzle with olive oil, tossing to coat. Spread evenly. Using palm of hand, press potatoes to flatten to ½-inch thickness. Sprinkle everything with za’atar and salt.
Roast in top and lower thirds of oven until edges are golden brown, flipping vegetables and rotating and swapping pans halfway through, about 30 to 35 minutes.
Herb Sauce
In food processor, combine cilantro, parsley, feta, lemon juice, olive oil, garlic and salt. Pulse until minced. With food processor running, drizzle in water, 1 tbsp at a time, until a smooth, slightly runny sauce forms, scraping down sides.
To serve
In bowl, toss mixed greens with just enough herb sauce to lightly coat (about ⅓ cup). Divide greens, cauliflower and potatoes, herb sauce and hummus among shallow bowls. Garnish with the pickled red onions and pistachios (if using) and more feta.