Slice the leeks, discarding the thick green pieces at their ends. In a large skillet, melt the salted butter over medium-high heat and add the minced garlic. Cook until the leeks are softened.
Transfer the softened leeks and garlic into your slow cooker. Add in your peeled or unpeeled Yukon gold potatoes along with bay leaves, thyme, salt, and black pepper.
Pour in the chicken broth until everything is submerged. Securely close the lid on your slow cooker and set it to cook on high for 5 hours or low for 8 hours.
Once your cooking time is up and the potatoes have softened considerably, remove any fresh thyme sprigs and bay leaves from the pot. Using an immersion blender, blend until you reach your desired consistency.
Stir in heavy cream for that luscious finish. Serve hot, garnished with freshly chopped chives, alongside crusty bread for dipping.