In a large pot, heat the vegetable oil over medium heat. Add the diced onion and sauté for about 3-4 minutes until softened.
Stir in the minced garlic and grated ginger, cooking for an additional minute 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, then stir in the red curry paste and fish sauce. Bring the mixture to a gentle simmer.
Add the shredded chicken and snap peas to the pot, cooking for about 5 minutes until the snap peas are tender.
Stir in the lime juice and season with salt and pepper to taste.
Remove from heat and garnish with chopped cilantro. Serve hot with lime wedges on the side.