Put the potatoes in a large stock pot of salted cold water. Cover and bring to boil over medium heat. Lower the heat to a simmer and cook until tender. Once the potatoes are cooked, pour them into a strainer, removing all of the water. Put them back into the original pot. If there is still a lot of excess water in the potatoes, put the pot over low heat, shaking the pot so the potatoes dry off but not burn. Turn off the heat, cover and keep warm.
In a large stock pot, over medium-high heat, add 2 tablespoons of butter and 1 tablespoon canola oil. When the butter has melted, add the onions, shallots and carrots. Turn the heat down to medium-low, and cook the vegetables until they soften, without burning or caramelizing. Saute for approximately 5 minutes, then add 2 quarts of vegetable stock. Keep the stock at a low simmer for about 30 minutes. Taste the stock and season with kosher salt and black pepper, to taste.
While stock is cooking, make Garlic Confit for croutons:
In a small saucepan over medium-low heat, add canola oil and whole peeled garlic. Allow to cook until very tender to the touch, about 30 to 45 minutes. It should be like roasted garlic where you can smash and spread it. Allow the garlic to cool a bit then remove garlic cloves from oil and smash the garlic making it look like a puree. Set aside.
Pour half of the stock into the pot of cooked potatoes. Using a hand mixer or immersion blender, puree the potatoes. Continue to add stock accordingly until the puree is thick but still pourable. Make sure the whole mixture is smooth. If the soup is still too thick, add more stock. Strain the soup in a fine mesh sieve; this is going to help remove the starchy, grainy feel from the potatoes. Strain the soup at least twice to get a nice smooth texture.
Add the strained soup to a fresh clean pot and put it over medium-low heat. Whisk in the 1 cup of the half-and-half, 1/2 a cup of heavy cream and 3 tablespoons of butter. (This is where your palette is going to come into play, you can make this as smooth and buttery as you want.) Season with kosher salt and white pepper. Keep whisking and stirring, so as not to let the soup burn. Lower the heat and keep the soup warm.
To make the garlic croutons:
Preheat oven to 375 degrees F.
Brush the garlic oil on both sides of the bread slices. Arrange them on a sheet pan and put in the oven to toast on both sides. Remove from oven and spread prepared garlic confit on top.
Assembly: Using a 4-ounce ladle, pour a ladle of soup into each bowl and squeeze a nice large circle of chive oil around the soup. Squeeze another large circle of beet reduction directly on top of the chive oil. Put 1 garlic crouton in the middle of each bowl. Garnish the croutons with a sprinkle of finely chopped chives.
Fill a bowl with ice and water. Bring a medium saucepan of water to a boil over medium heat. Once the water is at a boil, hold the bunch of chives with a pair of tongs. Put the chives into the water for 3 seconds and immediately remove to the ice water. Drain and dry the chives with a paper towel.
In a blender add chives and oil and puree until smooth and thoroughly blended. Allow the mixture to sit overnight, then strain to remove any chive particles. Strain again through 4 layers of cheesecloth. Pour into a squeeze bottle and when ready to use, put the bottle into hot water to bring to room temperature.
Puree the beets with a little bit of water in blender. Strain through a mesh strainer into a saucepan. Heat beet juice slowly over low heat and add the lemon juice. Pour the mixture through a fine mesh sieve and put it into a squeeze bottle.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.