Prep the potatoes: Peel and dice the potatoes into small, even cubes.
Smaller pieces cook faster and blend more smoothly.
Load the slow cooker: Add potatoes, onion, garlic, broth, salt, pepper, thyme, and bay leaf to the slow cooker. Stir to combine.
Cook low and slow: Cover and cook on Low for 6–8 hours or on High for 3–4 hours, until the potatoes are very tender.
Remove the bay leaf: If you used one, take it out before blending.
Mash or blend: For a chunky soup, use a potato masher to mash some of the potatoes right in the pot. For a smoother soup, use an immersion blender and blend to your preferred texture.
Leave some chunks if you like.
Thicken if needed: If you want a thicker soup, stir in the cornstarch slurry. Cover and cook on High for 10–15 minutes until slightly thickened.
Finish with dairy: Stir in the butter, milk, and cream. If using cheddar, add it now and stir until melted.
Taste and adjust salt and pepper.
Serve: Ladle into bowls and top with chives, bacon, extra cheese, a dollop of sour cream, and a crack of pepper.