Sauté aromatics: Heat olive oil or coconut oil in a pot or braiser over medium-high heat. When oil shimmers, add diced onion, (optional) diced green chilis, minced garlic and grated ginger and sauté for 5–6 minutes, until onions are translucent.
Add spices: Stir in curry powder. Cook, stirring often, for about 30 seconds to toast the spices. You can add a splash of water if needed to distribute the curry powder.
Add lentils and liquids: Pour in crushed tomatoes, rinsed lentils, and vegetable broth (or water). Stir well and bring to a boil.
Cook lentils: Reduce heat to medium-low to establish a very rapid simmer. Simmer uncovered for 25–30 minutes (stirring occasionally to keep things from sticking to the bottom of the pan), until lentils are tender.
Stir in coconut milk: Stir in the coconut milk, and simmer for another 5–10 minutes, stirring occasionally, until thickened to your preference. I like a thicker curry so I tend to simmer for a full 10 minutes. Season with salt and pepper to preference.
Serve: Spoon into bowls, garnish with fresh cilantro and fresh lime wedges if desired. Serve with steamed basmati rice or homemade vegan naan.