Prepare the Vegetables:
Slice the carrots, zucchini, and bell peppers into thin strips. Cube the eggplant, and trim the snap peas or green beans. Set aside.
Cook the Aromatics:
In a large pot or wok, heat the vegetable oil over medium heat. Add the red curry paste and cook for 1-2 minutes, stirring constantly, until fragrant.
Add Coconut Milk and Broth:
Stir in the coconut milk and vegetable broth. Bring to a simmer, then add the soy sauce, brown sugar, ginger, and garlic. Let the curry simmer for 5-7 minutes.
Cook the Vegetables:
Add the sliced carrots and cubed eggplant to the curry and cook for 5 minutes. Then, add the zucchini, bell pepper, and snap peas or green beans. Cook for another 5-7 minutes until the vegetables are tender but still slightly crisp.
Finish the Curry:
Stir in the lime juice and fresh basil. Taste the curry and adjust the seasoning, adding more soy sauce, sugar, or lime juice as desired.
Serve and Garnish:
Serve the curry over steamed jasmine rice. Garnish with cilantro, lime wedges, and crushed peanuts for extra flavor and texture.