Heat olive oil in a large stockpot or Dutch oven over medium-high heat. Add garlic, onion, bell pepper, and sweet potato. Sauté for 3-4 minutes, stirring occasionally, until vegetables begin to soften.
Stir in red curry paste and cook for 1 minute until darkened and fragrant. This blooms the spices for deeper flavor.
Pour in coconut milk and vegetable stock. Whisk gently to combine into a smooth, creamy broth with no clumps.
Bring the mixture to a boil. Add frozen potstickers one at a time. Reduce heat to maintain a gentle simmer.
Cook for 6-8 minutes until soup thickens slightly and potstickers are heated through and pillowy. Test one by cutting open to ensure the filling is hot.
Stir in fresh spinach and lime juice. Cook for 1-2 minutes until spinach is just wilted but still bright green.
Taste and adjust seasoning with additional lime juice, salt, or curry paste as needed. Different brands vary in spice level.
Ladle into deep bowls, garnish with fresh cilantro, and serve immediately with lime wedges and chili oil on the side.