Preheat your oven to 400°F (200°C). Spread the peeled and cubed sweet potatoes and chopped carrots on a baking sheet, drizzle with a tablespoon of olive oil, and toss to coat evenly. Roast in the oven for about 25-30 minutes until the vegetables are tender and slightly caramelized around the edges.
While the vegetables are roasting, heat a small drizzle of olive oil in a large pot over medium heat. Add the minced garlic and sauté until fragrant, about 1-2 minutes, being careful not to burn it. The garlicky aroma should fill the kitchen and the garlic should turn a light golden color.
Once the roasted vegetables are ready, transfer them into the pot with the sautéed garlic. Pour in the vegetable broth and bring the mixture to a gentle simmer. Let it cook together for about 10 minutes to allow the flavors to meld.
Remove the pot from heat and use an immersion blender to puree the soup directly until smooth. Alternatively, transfer the mixture in batches to a blender, blend until creamy, then return to the pot. The soup should be velvety and vibrant orange in appearance.
Taste the soup and season with salt and pepper as needed. If the soup feels too thick, stir in a splash of warm broth or water to loosen it to your desired consistency. Warm the soup gently over low heat if necessary, stirring occasionally.
Serve the soup hot, garnished with a drizzle of olive oil or fresh herbs if desired. The final texture should be silky and smooth, with a natural sweetness and vibrant color that invites spoonfuls of comfort and warmth.