Preheat oven to 350 degrees F.

Peel and grate carrots and parsnips - using the food processor is easiest. Place in a large bowl.

Combine 2 tablespoons flour with 1/2 cup Parmesan cheese. Stir into the vegetables.

Melt butter in a medium saucepan. Stir in 1/4 cup flour and cook for 2 minutes stirring constantly. Gradually stir in milk and continue to heat and stir until it starts to bubble. Remove from heat.

In a small bowl beat eggs with whipping cream and seasonings. Gradually stir into hot milk mixture. Stir for 1 minute.

Pour milk mixture over vegetables and stir well to combine.

Pour into a buttered 9 by 13 inch baking dish. Sprinkle with remaining Parmesan cheese.

Bake, uncovered, for about 1 hour, until golden and bubbly.