Preheat the oven to 400 degrees F.
Melt the butter in a 6-quart stock pot over medium-high heat. Add the onions and celery. Season with salt and pepper. Saute until the vegetables are soft, about 4 minutes. Add the bay leaf and garlic.
Add the stock and parsnips and bring the mixture to a boil. Reduce the heat to medium and simmer, uncovered, until the parsnips are very soft, about 1 hour. Remove soup from heat and allow to cool a little. Discard bay leaf.
Using a hand-held blender, carefully puree soup until smooth. Stir in cream. Season with salt and pepper.
In a small saute pan, over medium heat, render bacon until crispy. Remove the bacon and drain on paper towels. Fry the potatoes in bacon fat until crispy and brown, about 3 to 4 minutes. Transfer potatoes to paper towel lined plate when done. Season with salt.
To serve, ladle the soup into serving bowls. Garnish with the crispy potatoes, bacon and chives.