Combine the brown rice and water in a medium saucepan. Bring to a boil, then reduce heat, cover, and simmer for 40 minutes until the rice is tender. Remove from heat and let it sit covered.
Heat the vegetable oil in a large skillet over medium heat. Add the diced onion and cook for 3 minutes until it softens.
Stir in the minced garlic and grated ginger. Cook for 1 minute until fragrant.
Add the Thai red curry paste and stir for 30 seconds to coat the vegetables.
Pour in the coconut milk and bring the mixture to a gentle simmer.
Add the sliced red bell pepper, zucchini, broccoli florets, and carrots. Cook for 8 to 10 minutes, stirring occasionally, until the vegetables are tender but still hold their shape.
Stir in the soy sauce and lime juice. Taste and add salt and pepper as needed.
Fluff the cooked brown rice with a fork and divide it among four bowls. Spoon the curry over the rice and top each serving with chopped cilantro.