Preheat the oven to 400°F (200°C). Spread the quartered tomatoes and whole garlic cloves on a baking sheet. Drizzle with olive oil and sprinkle with salt and pepper. Roast in the oven for about 25-30 minutes until the tomatoes are caramelized and fragrant.
Transfer the roasted tomatoes and garlic into your slow cooker. Tear some fresh basil leaves and add them for extra flavor. Pour in the vegetable broth if you prefer a thinner soup or leave it out for a richer base.
Cover and cook on low for 4 hours, allowing the flavors to meld and deepen. The aroma will be warm and inviting as the ingredients gently simmer together.
Carefully remove the basil stems and discard. Using an immersion blender or regular blender, blend the mixture until smooth and velvety. Be cautious of hot splashes when blending.
Return the blended soup to the slow cooker or transfer to a pot. Taste and adjust the seasoning with additional salt and pepper if needed.
Warm the soup just until steaming, then serve garnished with freshly chopped basil leaves. Enjoy with crusty bread for a satisfying meal.