Slice the leeks into 1/2-inch rounds, using only the white and light green parts, and rinse thoroughly between layers to remove any trapped soil. Peel and cut potatoes into 1-inch chunks. Mince the garlic. Add all ingredients—leeks, potatoes, garlic, butter, salt, thyme, chili flakes, bay leaf, and broth—directly to your slow cooker. I like to add the bay leaf last so it sits on top and is easy to find later. Stir gently to combine, making sure the butter is distributed throughout.
Cover and cook on low for 8 hours until the potatoes and leeks are completely tender and falling apart. The long, gentle cooking allows the flavors to meld beautifully and creates a naturally creamy texture as the potatoes break down. You'll know it's ready when a fork easily pierces the potatoes with no resistance.
Carefully remove and discard the bay leaf from the cooked soup. Working in two batches to avoid overfilling your blender, transfer the soup to a blender and puree until smooth and creamy. I recommend leaving the slow cooker on warm while you blend so everything stays hot. Return each batch to the slow cooker as you finish blending, stirring to combine.
Stir in the heavy cream until fully incorporated—this adds a luxurious, silky texture that transforms the soup. Taste and adjust seasonings as needed, adding a pinch more salt or a crack of black pepper to your preference. Ladle into bowls and serve hot.