Heat the vegetable oil in a large skillet or heavy-bottomed pot over medium heat.
Add the chopped onion and cook for 4–5 minutes, until softened and lightly golden.
Add the minced garlic and grated ginger and cook for another 30–60 seconds.
Add curry powder, cumin, coriander, turmeric, paprika, and cayenne pepper if using.
Stir continuously for about 30 seconds to toast the spices.
Add the pumpkin puree and stir well to combine with the spiced onion mixture.
Cook for approximately 2 minutes.
Add diced tomatoes, coconut milk, and vegetable broth.
Season with salt and black pepper.
Stir until everything is well combined.
Bring the curry to a gentle simmer.
Reduce the heat to medium-low and cook uncovered for 15–20 minutes, stirring occasionally.
If the sauce becomes too thick, add a little extra vegetable broth or water.
Stir in the lime juice.
Add brown sugar or maple syrup if you want to balance the natural earthiness of the pumpkin.
Simmer for another 2–3 minutes.
Taste and adjust the salt, spices, and chili according to preference.
Stir in fresh cilantro.
Serve hot over basmati rice or alongside warm naan.