Heat olive oil in a large, heavy-bottomed soup pot over medium heat.
Add the sliced leeks and chopped fennel.
Sauté for about 8 minutes, until softened and just beginning to brown.
Stir in the chopped parsnips, garlic, sea salt, white pepper, herbes de Provence, and ground fennel seed.
Cook for one minute until fragrant.
Pour in the vegetable broth and 1½ cups / 360 ml (12.2 fl oz) of water. Increase the heat to bring the mixture to a boil.
Once boiling, reduce the heat to low, cover the pot, and let it simmer for 25 to 30 minutes, or until all the vegetables are very tender.
Remove the pot from the heat.
Stir in the milk and yogurt.
Carefully blend the soup until completely smooth and creamy, either with an immersion blender directly in the pot or by transferring it in batches to a standard blender.
Return the soup to the pot if necessary.
Stir in the fresh lemon juice to brighten the flavors.
Ladle the soup into bowls, garnish with the reserved fennel fronds, and serve immediately.