Heat coconut oil in a large pot over medium heat. Add onion, garlic, and ginger. Cook until fragrant, about 3 minutes.
Add red curry paste and cook for another minute, stirring constantly.
Add bell pepper, mushrooms, carrots, and broccoli. Stir to coat with curry paste and cook for 5 minutes.
Pour in coconut milk, vegetable broth, soy sauce, and brown sugar. Bring to a boil, then reduce heat and simmer for 15 minutes or until vegetables are tender.
Add snap peas and cook for an additional 2 minutes.
Remove from heat and stir in lime juice and basil leaves.
Taste and adjust seasoning with salt if needed.
Serve hot, over rice noodles if desired.