Cook basmati rice according to package instructions; keep warm.
Heat olive oil in a large pot over medium heat.
Sauté onion, garlic, and ginger until fragrant, about 3 minutes.
Stir in curry powder, cumin, turmeric, and chili powder; cook 1 minute.
Add tomato paste, crushed tomatoes, and broth; stir well.
Mix in red lentils; bring to a boil.
Lower heat, cover, and simmer 20 minutes until lentils are tender.
Stir in coconut milk, salt, and pepper; cook 5 minutes more.
Serve curry hot over rice, garnished with cilantro.