Peel and chop the sweet potatoes and carrots into uniform 2.5 cm cubes, creating vibrant orange chunks ready to cook.
Dice the onion finely and mince the garlic, filling your kitchen with a fragrant aroma as you prepare the base.
Heat the olive oil in a large heavy-bottomed pot over medium heat until shimmering and fragrant.
Add the diced onion and minced garlic to the hot oil, sautéing for about 5 minutes until translucent and fragrant, with a slight sizzle and the aroma turning sweet and savory.
Stir in the chopped sweet potatoes and carrots, cooking for another 2-3 minutes until their edges begin to turn golden and their colors deepen.
Sprinkle the cumin and coriander over the vegetables, toast briefly for about 30 seconds until the spices release their aroma and turn slightly darker.
Pour in the vegetable broth, bringing the mixture to a gentle simmer. Cover loosely and cook for 20-25 minutes until the vegetables are very tender and easily pierced with a fork, filling the kitchen with a warm, earthy scent.
Remove the pot from heat and use an immersion blender to blend the soup directly in the pot until silky smooth, or carefully transfer in batches to a blender and puree.
Stir in the coconut milk, blending until fully incorporated for a velvety, bright-orange finish, and season with salt and pepper to taste.
Reheat gently if needed, and serve the soup hot, garnished with a drizzle of coconut milk or a sprinkle of herbs for extra color and flavor.