Heat the oil in a large pot over medium heat. Add the diced onion and cook for 3-4 minutes until softened but not browned.
Add the minced garlic and grated ginger to the pot and cook for another minute until fragrant. Be careful not to burn the garlic, as it can turn bitter.
Stir in the Thai red curry paste and cook for 1-2 minutes to wake up the spices. You’ll know it’s ready when the paste becomes aromatic and slightly darker.
Add the pumpkin puree and vegetable broth, stirring to incorporate the curry paste completely. Bring the mixture to a gentle simmer.
Simmer the soup for about 10 minutes, allowing the flavors to meld together. The pumpkin should be fully incorporated with the broth.
Pour in the coconut milk and stir well to combine. Return to a simmer but do not boil rapidly, as this can cause the coconut milk to separate.
Add the fish sauce, brown sugar, and lime juice, then taste and adjust seasonings. The soup should have a balance of sweet, spicy, tangy, and savory notes.
For a silky-smooth texture, blend the soup using an immersion blender directly in the pot, or carefully transfer in batches to a standard blender (allow to cool slightly first if using a standard blender).
Return the soup to the pot if you used a standard blender, warm it through if needed, and do a final seasoning check.
Serve hot in bowls with your choice of garnishes: a swirl of coconut milk, fresh cilantro leaves, sliced red chili for extra heat, and toasted pumpkin seeds for crunch.