Preheat the oven to 400 degrees.
Slice each vegetable thin using a knife or a mandolin and add to 3 separate bowls.
Add 2/3 cup of the heavy cream and 2 oz of the parmesan to each bowl.
Add some of the thyme to each bowl and the salt and pepper. Toss to evenly coat.
Place the sliced vegetables into the cast iron skillet by color.
Pour what was left of the heavy cream mixture from the parsnips and sweet potato bowl over the sliced veggies.
Do not use the beets mixture as it will be too pink.
Cover and bake in the oven for 40-45 minutes.
Remove cover and top with the rest of the parmesan and the gruyere.
Place under broiler for a few minutes to create a crispy and golden cheese layer on top.
Garnish with fresh thyme and enjoy!