Cut the leeks in half lengthwise, rinse well, and thinly slice the white and light green portions. Heat the olive oil over medium-high heat in a large heavy-bottomed pot and add the leeks. Saute for 10 minutes until softened and beginning to brown. Season with salt and pepper.
Add the potatoes, vegetable stock, water, and thyme springs and bring to a boil. Reduce the heat and let simmer for 25 minutes, or until the potatoes are softened.
Remove the thyme sprigs; add the soup in batches to a food processor or blender and puree until smooth. (NOTE: Be careful of the hot liquid!! Make sure to hold down the lid with a thick towel so you don’t get burned!) Return the soup back to the pot and stir in the cream, thyme leaves, and parsley. Season generously with salt and pepper.
Garnish with a dollop of creme fraiche and a parsley sprig. Serve hot with crusty bread for a perfect winter day treat!