1. Preheat oven to 350F. Generously butter a 8x11 oval gratin dish (2 qt). In a small bowl, combine, croutons, Parmesan, and thyme for topping; set aside.
2. In a medium saute pan, heat olive oil over med-high heat. Add onion and cook until translucent, 2-3 min. Add garlic and cook 3 minutes. Add root vegetables and cook 2 minutes. Season generously with salt and pepper. Add the stock and bring to a boil. Lower heat and simmer, covered, until just tender, about 10 min. Set aside for 5 min to cool a little.
3. In a large bowl, whisk together the eggs and cream. Stir in the rice, ricotta, mozzarella, and Parmesan. Add one cup of the hot vegetable mixture and stir to temper eggs. Add the remaining vegetable mixture, stirring until combined. Transfer to prepared gratin dish.
4. Place dish on baking sheet and bake until edges are set, but the center is still very loose, about 20 min. Remove from oven and stir well. Smooth the top, sprinkle bread-crumb mixture over gratin, and return to oven. Bake until custard is just set and top is golden, about 15-20 minutes. Let rest 5 min before serving.
