Start by heating the large pot over medium heat and add the olive oil. Once shimmering, toss in the diced onion and sauté for about 5 minutes until it becomes translucent and fragrant, filling your kitchen with a sweet aroma.
Add the peeled and chopped sweet potatoes and carrots to the pot. Stir them around with the onions, allowing their edges to start softening and releasing a gentle, earthy scent. Cook for about 2 minutes to get the veggies coated with the flavors.
Pour in the vegetable broth, enough to cover the vegetables. Bring the mixture to a gentle simmer, then reduce the heat to low. Cover the pot and let everything cook for about 20-25 minutes until the sweet potatoes and carrots are tender and easily pierced with a fork, filling your kitchen with a simmering, comforting smell.
Once the vegetables are soft, remove the pot from heat. Carefully use an immersion blender to blend the soup directly in the pot until it’s silky smooth, or transfer it in batches to a blender. Blend for 1-2 minutes until the mixture is velvety and uniform in texture.
Return the blended soup to a gentle simmer, then season with salt and pepper to taste. Add a splash of lemon juice to brighten the flavors and stir well to incorporate.
Ladle the warm, velvety soup into bowls, and optionally garnish with a drizzle of olive oil or a dollop of yogurt. Serve immediately, savoring the rich aroma and smooth texture that make this dish so cozy and satisfying.