Preheat your oven to 400°F (200°C). Arrange chopped sweet potatoes and sliced fennel on a baking sheet, drizzle with olive oil, and toss to coat evenly. Roast for 30-35 minutes until the edges are caramelized and tender.
While the vegetables are roasting, heat a large pot over medium heat. Add a splash of olive oil and sauté the minced garlic until fragrant and just beginning to turn golden, about 1 minute.
Once the garlic is aromatic, add the roasted sweet potatoes and fennel to the pot. Pour in the vegetable broth and stir to combine. Bring the mixture to a gentle simmer, allowing the flavors to meld for about 10 minutes.
Use an immersion blender directly in the pot or transfer the mixture carefully to a blender. Blend until smooth and creamy—anywhere from 30 seconds to a minute—then return to the pot if blended externally.
Taste the soup and season with salt, pepper, and chopped fresh thyme. If desired, add a splash of lemon juice or vinegar to brighten the flavors. Adjust seasoning to your liking.
Warm the soup gently over low heat if necessary, ensuring it's hot and ready to serve. The finished soup should be thick, velvety, and vibrant in color, with a luscious, rustic texture.