Heat oil in a medium-sized wok. Add the curry paste and saute for 30 seconds. Stir in the coconut milk and mix well.
Add onion, potatoes, cashews, and salt. Add ½ cup of water, give a quick stir, and cook covered for 10 to 15 minutes on medium heat. Cook until the potatoes are cooked soft and tender and can be easily cut with a fork.
Stir in soy sauce, brown sugar, broccoli, peppers, and snow peas. Cook for 4 to 5 minutes on medium-high heat or just until the curry comes to a gentle boil.