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1
In a large pot or Dutch oven set over medium heat, add just enough olive oil to cover the bottom of the pot. When the oil is hot, add the onions and cook until they begin to soften and turn translucent, stirring occasionally. Season with a small pinch of salt.
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2
Add the celery root, season with a pinch of salt, and continue to cook for approximately 5 minutes, stirring occasionally. While the celery root is cooking, peel and core the apples, and cut them into thin slices.
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3
Peeling, coring, and slicing the apples probably took you about 5 minutes, so add the apples now. Continue to cook, stirring frequently, for 3 minutes. Add the garlic, cayenne, white pepper, bay leaves and tarragon sprigs. Give everything a stir. Add the white wine, turn the heat up to high, and cook until the liquid has almost entirely evaporated, stirring occasionally. Add the water, bring the soup to a simmer, then lower the heat so that the soup maintains a slow simmer. Gently cook the soup until the celery root is very soft. To test how soft the celery root is, stab it with a fork from time to time.
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4
When the celery root is ready, turn off the heat and remove the bay leaves and tarragon sprigs from the soup. Working in batches, transfer the soup to a blender, and blend on high speed until the soup is velvety smooth. If the soup is looking too thick, add a little water as necessary until you've achieved a better consistency. When all of the soup is blended, taste it. Adjust as necessary with salt, cayenne, and white pepper. To serve, garnish each bowl with some chopped tarragon and a drizzle of your best olive oil.
