Heat the vegetable oil in a large pot over medium heat. Add the chopped onion and sauté until translucent, about 5 minutes.
Stir in the minced garlic, grated ginger, and red curry paste. Cook for an additional 2 minutes until fragrant.
Pour in the chicken or vegetable broth and bring to a simmer.
Add the coconut milk, sliced mushrooms, red bell pepper, and snap peas or green beans. Simmer for 10-15 minutes until the vegetables are tender.
Stir in the soy sauce and lime juice. Taste and adjust seasoning if necessary.
Serve hot, garnished with fresh cilantro and lime wedges on the side.