Preheat the oven to 400 degrees F. Heat the olive oil in a large nonstick skillet over medium heat, add the onions and cook, stirring occasionally, until just browned and soft, about 5 minutes. Add the kale, garlic and 1/2 teaspoon each salt and pepper and cook until the kale is bright green, about 2 minutes. Add the broth and continue to cook until the kale is wilted and most of the broth is absorbed, about 5 minutes more. Add the squash, zucchini and 1/2 teaspoon salt and toss to combine with the kale. Continue cooking until the squash begins to soften, about 8 minutes. Remove from the heat and stir in the mayonnaise.
Toss the cooked vegetables, brown rice, cheeses, 1/2 cup of the bread crumbs and the egg in a large bowl until mixed. Spray a 9-inch square or 2-quart casserole dish with cooking spray. Spread the mixture in the bottom of the casserole and top with the remaining 1/2 cup bread crumbs, 1/4 teaspoon salt and a few grinds of pepper. Bake until the squash and zucchini are tender and the top is browned and crisp, about 35 minutes. Serve hot.
Make-Ahead Tip: Freeze the baked casserole for up to 2 weeks. Cover with foil and reheat at 350 degrees F until hot, 35 to 45 minutes.
Copyright 2013 Television Food Network, G.P. All rights reserved