Preheat your oven to 400°F (200°C). Slice the top off the garlic bulb to expose the cloves and drizzle with olive oil. Wrap it in foil and roast for about 40 minutes until soft and fragrant.
Meanwhile, peel and dice the potatoes into roughly 1-inch pieces, then place them in the slow cooker.
Once the garlic is roasted and cool enough to handle, squeeze out the tender roasted cloves into a small bowl, mashing them slightly to release their sweet aroma.
Add the mashed roasted garlic to the slow cooker with the potatoes, along with the vegetable broth.
Cover the slow cooker and cook on low for 6 hours, or until the potatoes are very tender and starting to fall apart.
Use an immersion blender directly in the slow cooker to blend the soup until it's completely smooth and velvety. Alternatively, carefully transfer in batches to a blender and blend until creamy.
Stir in a splash of cream or sour cream for richness, then season with salt and pepper to taste.
Simmer the soup uncovered for an additional 10 minutes to let the flavors meld and thicken slightly.
Taste again and adjust the seasoning as needed, then ladle the hot, creamy soup into bowls.
Garnish with additional sour cream, chopped herbs, or a drizzle of olive oil if desired. Serve piping hot and enjoy its comforting warmth.
