Season shrimp with salt, pepper, cayenne pepper, and lime juice. Let marinate for 10 minutes.
Drizzle oil in a large skillet and heat over medium. Add the onions and cook for 3 minutes. Add in the bell peppers and cook another 2 minutes. Add the sugar snap peas, garlic, ginger, and seasonings. Cook for about 30 seconds and then pour in the coconut milk and brown sugar.
Bring to a simmer and then add in the shrimp. Bring back to a simmer and cook for about 5 minutes until shrimp is pink and cooked through.
If desired, stir in fish sauce and for a thickened sauce, add in the corn starch water mixture and cook another minute.
Serve curry over rice and garish with cilantro or thai basil.