Warm oil in a soup pot over medium heat.
Stir in ginger, garlic, and curry paste. Cook until fragrant, about 1 minute.
Whisk in broth and bring to a gentle simmer.
Add coconut milk, soy sauce, fish sauce, sugar, salt, and pepper. Simmer 2 minutes.
Add mushrooms, bell pepper, and green onions. Simmer until just tender, 4 to 5 minutes.
Slide in frozen dumplings. Simmer until cooked through and floating, 5 to 6 minutes.
Stir in spinach and sesame oil. Cook until wilted, about 1 minute.
Off heat, add lime juice and cilantro. Taste and adjust seasoning.
Ladle into bowls and drizzle chili oil if you like heat.