Preheat oven to 350°.
Wash and scrub the baby beets, removing the greens about an inch above the beet.
Cover the inside of a large ovenproof skillet with about 1" of rock salt.
Put the beets on top of the rock salt and bake for about 30-45 minutes depending on the size of the beets. You will want them to be tender to the point that a toothpick could be easily inserted into them.
Also while the beets are roasting, peel the ginger and slice 16 very thin pieces lengthwise using a mandoline.
Then, with a french knife, cut the ginger into a julienne. There should be a small piece of ginger left which should be set aside for later use.
In a small saucepot heat the grapeseed oil to 250° and add the ginger, fry until golden brown.
Remove the ginger from the oil and place onto a paper towel, sprinkle with salt and set aside.
Allow the oil to cool, it will have acquired a nice ginger flavor and you will use it to cook the fish for this dish.
Transfer the ginger infused grapeseed oil into a small pan large enough to hold the four pieces of halibut. Make sure they are covered with oil.
Cool the oil to about 225-230° and add the thyme and bay leaf. Allow the herbs to infuse.
Prepare the ginger vinaigrette while the oil is cooling.
Remove the beets from the oven and allow them to cool until you can handle them with your hands.
Peel the beets and place them in mixing bowls keeping each color separate.
Marinate the beets with the ginger vinaigrette. Reserve some vinaigrette for dressing.
Season the halibut with salt and fresh ground pepper.
Place the seasoned halibut into the warm ginger and herb-infused grapeseed oil.
The fish should take about 8-10 minutes to cook.
While the fish is cooking, arrange a nice mixture of beets on four plates.
Dress the arugula with the remaining ginger vinaigrette and scatter it over the beets.
When the fish is cooked, remove it from the oil and place it on top of the baby beets and arugula.
Garnish with the fried ginger.