Melt butter in a medium pan over medium heat. Add onions; cook, stirring, until soft but not browned, about 6 minutes. Add wine; simmer until reduced by half, about 2 minutes. Add celery root, thyme sprigs, broth, and water; bring to a simmer. Cook, uncovered, until celery root is soft, about 20 minutes.
Remove from heat, and discard thyme sprigs. Transfer to a food processor; puree until smooth. Return soup to pan; stir in cream. Place over medium heat until heated through. Season with salt and white pepper. Reduce heat; keep warm until serving.
To serve, spoon into 4-ounce cups; top each with a small dollop, about 1 teaspoon, of creme fraiche.
To serve soup as an hors d'oeuvre, spoon 1/4-cup servings into small glasses or cups for guests to drink.