Preheat the oven to 400°F. In a large bowl, toss the cauliflower with the oil and ½ tsp. salt and ½ teaspoon pepper. Spread on a baking sheet and roast until tender and lightly browned, about 20 minutes. Let cool slightly, finely chop, and transfer to a medium bowl.
Add the quinoa, corn, flour, scallions, zest, parsley, feta, eggs, salt and pepper to taste, and mix well. Using about ½ cup of the mixture, form into 6 patties, about ½-inch thick. Place on a foil or parchment lined baking sheet. Brush the cakes with olive oil. Bake until lightly golden, about 20 minutes.
Meanwhile, in a small bowl, mix the yogurt, lemon juice, and mint. Season with a pinch of salt and pepper.
Serve the cakes with cucumber, feta, scallions, and the yogurt sauce.