Melt butter in a stock pot or Dutch oven over medium heat. Add the leeks and cook, stirring occasionally, until tender, about 10 minutes. Add the garlic and cook, stirring, for 30 seconds. Add the potatoes, broth, thyme, and bay leaves and bring to a simmer. Simmer uncovered until the potatoes are tender, about 15 minutes. Remove the thyme sprigs and bay leaves.
Working in batches, blend the soup until smooth. Pour back into pot.
Whisk in the cream and collagen. Heat over medium-low heat until hot. Season to taste with salt and pepper.