Heat vegetable oil in a large pot or Dutch oven over medium heat. Add red curry paste, ginger, and garlic; sauté for 2 minutes until fragrant.
Whisk in the coconut milk and chicken broth until the curry paste is fully incorporated. Add fish sauce and brown sugar, then bring the liquid to a gentle simmer.
Carefully add the frozen dumplings and sliced red bell pepper. Maintain a simmer for 8 to 10 minutes, or until the dumplings are heated through and floating.
Stir in the baby spinach and lime juice. Cook for 60 seconds until the spinach is just wilted.
Ladle into bowls and garnish with chopped cilantro and lime wedges. Serve immediately.