Heat the olive oil in a large pot over medium heat. Add the diced onion and cook for 5-7 minutes until translucent and slightly golden. This initial caramelization builds foundational flavor.
Add the garlic and ginger to the pot and sauté for 1 minute until fragrant. Be careful not to burn them, as they can quickly become bitter.
Stir in the curry paste, cayenne (if using), cumin, and coriander. Cook for about 30 seconds until the spices become aromatic, which blooms their flavors and removes any raw taste.
Add the pumpkin puree and broth, stirring to combine. Bring the mixture to a gentle simmer and cook for 15 minutes, allowing the flavors to meld together.
Pour in the coconut milk and maple syrup, then continue to simmer for another 5 minutes. The coconut milk adds creaminess while the sweetener balances the heat.
While the soup simmers, prepare the grilled-cheese croutons. Butter one side of each bread slice, then flip half the slices butter-side down and top with grated cheese. Cover with the remaining bread slices, butter-side up.
Cook the sandwiches in a skillet over medium heat for 2-3 minutes per side until golden brown and the cheese is melted. Transfer to a cutting board and let cool slightly.
Blend the soup until smooth using an immersion blender or in batches using a regular blender. If using a regular blender, be careful with the hot liquid and blend in small batches.
Season the soup with salt, pepper, and fresh lime juice to taste. The acid from the lime brightens all the flavors.
Cut the grilled cheese sandwiches into 1-inch squares to create the croutons.
Serve the soup hot, topped with grilled-cheese croutons and fresh cilantro if desired.