Heat the vegetable oil in a large pot over medium heat.
Add the chopped onion and cook until translucent, about 5 minutes.
Add the minced garlic and ginger, and cook for another minute.
Stir in the Thai red curry paste and cook for 2 minutes.
Add the coconut milk and vegetable broth, and bring to a simmer.
Add the bell pepper, carrot, and broccoli, and cook until tender, about 10 minutes.
Stir in the soy sauce and lime juice, and cook for another 2 minutes.
Remove from heat and stir in the fresh basil leaves.
Serve hot with rice or noodles.