Preheat oven to 350°F. and grease a 9.5-inch baking dish with olive oil. Set aside. In a large bowl combine sweet potato, parsnips, flour, sea salt, pepper, nutmeg, red pepper flakes, and dried thyme. Stir to combine.
Spread a layer of soup on the bottom on baking dish. Add one layer of sliced sweet potato and parsnips, overlapping slightly, to dish. Sprinkle with Parmesan cheese and a drizzle of soup. Repeat with the remainder of the sweet potatoes and parsnips, Parmesan cheese, and soup. Sprinkle the top of the gratin with Gruyère cheese.
Cover baking dish with foil and bake for 40 minutes. Remove foil, return to the oven, and cook an additional 30 minutes, or until Gruyère cheese is bubbly and browned and vegetables are fork tender. Remove from oven, cover with foil, and let sit 20 minutes. Garnish with fresh thyme and enjoy!