Make a tasty spread for the tilapia cakes: Combine equal parts plain Greek yogurt, mayo, and ketchup. Grown-ups might appreciate the addition of a little horseradish.
In a food processor, pulse the tilapia, egg, bread crumbs, salt, and pepper. Form into 8 patties. Heat the olive oil in a large, nonstick sauté pan over medium heat. Cook the patties 4 minutes per side, or until opaque.
In a steamer basket over boiling water, steam the broccoli until tender, about 5 minutes. In a large bowl, combine the broccoli, farro, pomegranate seeds, salad dressing, and salt to taste. Serve with tilapia cakes.