Heat oil in a large pot, over medium heat. Add the onion, turmeric root and ginger and sauté until golden, about 4 minutes.
Add garlic and curry powder and continue cooking, stirring about 2 minutes.
Add the carrots and parsnips, and cook for about another 5 minutes, stirring, until they start to warm up and blend with the other ingredients.
Add the vegetable broth and bring to a boil.
Cover, reduce heat and simmer for about another 20 minutes until the carrots and parsnips are tender.
Blend with an immersion blender, or in small batches in a high-speed blender. Be careful when using a traditional blender as hot contents create pressure.
Return the pureed mixture to the pot, and add the coconut milk, lime, and sugar. Return to just a simmer, give it one more stir, and remove the soup from the heat.
Check flavor for salt and pepper. Serve in soup cups with a sprinkle of sesame seeds for garnish.