Preheat your oven to 400°F (200°C). Slice the garlic head in half horizontally, drizzle the cut sides with olive oil, and wrap it in foil. Roast for about 30-40 minutes until the cloves are soft, fragrant, and caramelized.
While the garlic roasts, peel and dice the potatoes into even cubes. Prepare the vegetable broth and set aside.
Once the garlic is done, carefully squeeze out the soft, roasted cloves from their skins into a bowl. Mash them slightly with a fork to release the sweet, caramelized aroma.
Transfer the diced potatoes, roasted garlic, and vegetable broth into the slow cooker. Cover and cook on low for 6-8 hours until the potatoes are very tender and starting to break down.
Once cooked, use an immersion blender directly in the slow cooker to blend the soup until smooth and velvety, or carefully transfer in batches to a blender. Blend until creamy, then return to the cooker if needed.
Taste the soup and season with salt and pepper as needed, stirring well to incorporate the flavors. If desired, stir in a spoonful of sour cream for extra richness.
Serve the soup hot, garnished with additional sour cream, chopped herbs, or a drizzle of olive oil if desired. Enjoy the comforting aroma and silky texture with each spoonful.
