Step 1: Heat olive oil in a large pot or Dutch oven over medium heat. Add the chopped onion and cook until softened and translucent, about 5-7 minutes.
Step 2: Stir in the minced garlic, ground cumin, and turmeric. Cook for another minute until fragrant, being careful not to burn the garlic.
Step 3: Add the diced carrots and rinsed red lentils to the pot. Stir well to coat them with the aromatic mixture.
Step 4: Pour in the vegetable broth. Bring the mixture to a boil, then reduce the heat to low, cover, and simmer for 20-25 minutes, or until the lentils are tender and the carrots are soft. Stir occasionally.
Step 5: Once the lentils and carrots are cooked through, remove the pot from the heat. Carefully use an immersion blender to blend the soup directly in the pot until it reaches your desired level of creaminess. Alternatively, transfer the soup in batches to a regular blender and blend until smooth (use caution with hot liquids).
Step 6: Stir in the full-fat coconut milk, fresh lemon juice, salt, and black pepper. Return the pot to low heat and warm through gently for 2-3 minutes, but do not boil.
Step 7: Taste and adjust seasonings as needed. Ladle the creamy carrot lentil soup into bowls, garnish with fresh cilantro or parsley, and serve hot.