Preheat oven to 375 degrees F & lightly butter a deep cake pan 8 inches in diameter, then line the bottom of the pan with parchment paper.
In a large bowl mix together the breadcrumbs, cheese, herbs & garlic, then season to taste with salt & pepper, before sprinkling half of this crumb mixture over the bottom of the prepared pan.
Slice all vegetables as thinly as possible, which is best done with a mandoline or in a food processor with a thin cutting disc.
The vegetables are to be layered in the prepared pan ~ lightly seasoning with the crumb mixture every couple of layers ~ starting with half of the potatoes, then half of the parsnips, then half of the turnip, then half of the sweet potato & finally half of the rutabaga.
At this point sprinkle a little more than half of the remaining breadcrumb mixture over everything, then start the entire process again, finally topping the last layer with the remaining crumb mixture.
Whisk together the eggs, vegetable stock & cream then season lightly.
Pour this mixture evenly over the layered vegetables & cover with aluminum foil, pinching around the edges to seal.
Bake for 1 hour, then remove the foil & bake another 30 minutes.
Preheat the broiler to high, then turn the cake onto a heatproof plate. Remove & discard the parchment paper lining before placing the cake under the broiler for 4 or 5 minutes or until it is crisp & golden.
Let it cool just slightly, then cut into wedges & serve.