Start by washing and chopping all your vegetables, including the leek, yam, cabbage, green bell pepper, and snap peas. Mince the ginger and garlic, and chop chicken into bite-sized pieces or prepare shrimp.
In a large skillet or wok, heat the 3 tablespoons of oil over medium heat. Add the chopped leeks, and sauté for about 2 minutes until soft and fragrant. Add minced garlic and ginger, cooking for another minute.
Toss in yam cubes, chopped cabbage, green bell pepper, and snap peas. Stir well and let cook for about 5-7 minutes until vegetables are tender yet crisp.
Add red curry paste starting with 1 tablespoon, adjusting to taste. Stir into the vegetable mixture and cook for another minute.
Pour in chicken broth and coconut milk. Stir to combine and bring to a gentle simmer.
If using chicken, add it now and cook through for about 8-10 minutes. If using shrimp, add them to the simmering broth and cook until pink and opaque, about 3-4 minutes.
If a thicker curry is desired, mix cornstarch with a splash of water to create a slurry, then stir it into the curry. Cook for another minute until thickened.
Stir in fish sauce, lime juice, and brown sugar. Taste and adjust seasoning as needed.
Remove from heat and fold in Thai basil leaves. Serve hot, garnished with fresh cilantro over jasmine or white rice if desired.