Peel the pumpkin or squash, then cut it into uniform 2 cm cubes, aiming for smooth, even pieces.
Heat a tablespoon of oil in a heavy-bottomed pot over medium heat until it shimmers and starts to ripple.
Add the chopped onion and cook, stirring occasionally, until it becomes translucent and fragrant, about 5 minutes. You should hear a gentle sizzle and see the onions turn a soft, golden color.
Stir in the minced garlic, grated ginger, and turmeric, cooking for about 1 minute until fragrant. The mixture will become aromatic and slightly darker in color.
Gently add the pumpkin cubes to the pot, stirring to coat them with the fragrant spice mixture.
Pour in the can of coconut milk and add a splash of vegetable broth if needed to cover the pumpkin. Bring the mixture to a gentle simmer, watching for small bubbles to form around the edges.
Reduce the heat to low and let the curry simmer uncovered for 20-25 minutes, stirring occasionally. The pumpkin should become tender when pierced with a fork, and the sauce will thicken slightly, coating the cubes evenly.
Taste the curry and season with salt as needed. Squeeze in fresh lime juice for brightness and sprinkle chili flakes if you like some heat.
Remove the pot from heat and let the curry rest for about 5 minutes, allowing flavors to meld and develop further.
Serve the pumpkin curry hot over steamed rice, garnished with chopped cilantro for a fresh, fragrant finish.