In a large pot, heat the vegetable oil over medium heat. Add the diced onion and sauté for about 3-4 minutes until translucent.
Stir in the minced garlic and grated ginger, cooking for an additional 1-2 minutes until fragrant.
Add the sliced red bell pepper and mushrooms to the pot, cooking for another 3-4 minutes until they begin to soften.
Pour in the coconut milk and chicken broth, stirring to combine.
Add the fish sauce, lime juice, and red curry paste. Bring the mixture to a gentle simmer.
Stir in the shredded chicken and snap peas, cooking for another 5-7 minutes until heated through and the snap peas are tender-crisp.
Taste and adjust seasoning if needed.
Serve hot, garnished with sliced green onions and fresh cilantro. Offer lime wedges on the side for an extra burst of flavor.