Heat the oil in a large pot over medium heat and cook the onion until soft, about 5 minutes. Add the garlic and ginger and cook 1 minute.
Stir in the curry paste, cumin, and turmeric and cook for a full minute until the pot smells fragrant. This step is what separates a deep-tasting curry from a flat one.
Add the rinsed lentils and broth. Bring to a boil, then reduce to a simmer, cover, and cook 20 to 25 minutes until the lentils have completely fallen apart.
Stir in the coconut milk and warm through without boiling. Add the spinach and stir until just wilted.
Finish with the lime juice and salt. Taste and add more lime until it tastes bright rather than heavy.