If using fresh pumpkin, cut it in half, scoop out the seeds, peel the skin, and chop the flesh into small cubes. If using canned pumpkin puree, open the can and set it aside.
Heat sesame oil in a large pot over medium heat. Add minced garlic and ginger, and sauté for about 1 minute until fragrant.
Stir in red curry paste and cook for another minute. Then add pumpkin puree, coconut milk, vegetable broth, soy sauce, lime juice, brown sugar, salt, and black pepper. Stir well to combine.
Bring the mixture to a gentle simmer and cook for about 10-15 minutes, stirring occasionally. Use an immersion blender to puree the soup if a smoother texture is desired.
Taste and adjust seasoning if necessary. Serve hot, garnished with fresh cilantro.