In a small sauce pan over medium heat add cream and fresh thyme. Allow to simmer for about 15-20 minutes, or until it has reduced by half. Ensure you stir frequently to ensure it does not boil over. When reduced strain the thyme out with a fine mesh strainer.
Meanwhile, Place potato pieces and bay leaves into a large pot, and cover with enough water so that the water is 1 inch over the potatoes. Add enough salt to the water so that the water is similar to seawater. Place over medium-high heat and cook until potatoes are fork-tender.
Preheat oven to 425°Drain potatoes with a colander, and discard the bay leaves. Using a potato ricer or a masher, mash the potatoes back into the empty pot. Add butter, infused cream, sour cream, horseradish, ½ of the Bothwell Horseradish Cheese, and ½ of the aged white cheddar to the pot, and mix well until completely combined (using a hand-mixer makes very easy work of this!). Season with salt and pepper, and place into a baking dish. Sprinkle the top with the remaining cheese and place into the oven for 15-20 minutes, or until the cheese is bubbling and beginning to brown.