In a heavy pot over medium-low heat, pour in the oil, add the onion, carrot, garlic and bay leaf and simmer for 10 minutes so that the vegetables soften and the flavors deepen, caramelizing slightly. Meanwhile, prepare the celery root, potato and apple.
Once the the onion mixture has cooked, add the vegetables, pour over the water and stir in the tarragon, parsley, salt and pepper. Bring the mixture to a boil, lower to a simmer, cover with a lid and cook for 15 minutes. Turn off the heat, remove bay leaf and either blend with an immersion blender in the pot, or transfer to a heat-proof blender and blend until completely smooth. Pour the soup mixture back into the pot and add the cream. Stir to combine completely. Taste and adjust the seasonings, adding salt and pepper to taste, as needed. Finish with a drizzle of good quality extra virgin olive oil and a sprinkling of parsley or tarragon.