In a large pot or Dutch oven, heat the olive oil over medium heat. Add the ginger, garlic, cumin, chili flakes, and turmeric, and cook until fragrant, about 2 minutes, stirring constantly.
Add the carrots, tomatoes, lentils, salt, and broth, stirring until well combined.
Cover, bring to a boil, then reduce to a simmer. Simmer, covered, for 30-35 minutes, or until the carrots are soft and the lentils begin to soften and break apart, stirring occasionally.
Uncover and stir in the coconut milk, vinegar, and maple syrup, stirring to combine. Using an immersion blender, blend until just barely smooth. Alternatively, working in batches, carefully ladle the soup into a blender. Blend until just barely smooth, then return to the pot.
Taste and add additional salt or vinegar if desired. Serve with whatever toppings you enjoy.