Preheat your oven to 400°F (200°C). Place the whole garlic bulbs on a baking sheet, drizzle with a tablespoon of olive oil, and wrap loosely in foil. Roast for about 40 minutes, until the cloves are soft, fragrant, and golden around the edges.
While the garlic is roasting, peel and dice the potatoes into even chunks. This helps them cook uniformly and quickly.
Once the garlic is done roasting and cool enough to handle, squeeze out the soft roasted cloves into a small bowl, mashing them slightly with a fork until smooth.
Add the diced potatoes, mashed roasted garlic, vegetable broth, and a pinch of salt and pepper into your slow cooker. Stir gently to combine all the flavors.
Cover the slow cooker with the lid and set it to low. Let the soup simmer for about 5-6 hours, until the potatoes are very tender and the flavors meld into a fragrant, thickened broth.
Once cooked, gently mash some of the potatoes with a potato masher or the back of a spoon directly in the slow cooker to thicken the soup further. Adjust seasonings with salt and pepper as needed.
Serve hot, garnished with your favorite toppings or a drizzle of olive oil. The soup should be creamy, with a velvety appearance and an irresistible roasted garlic aroma.