In a large saucepan, heat the oil over medium-low. Add the broccoli and bell pepper; season with salt and pepper. Cover and cook until the vegetables begin to soften, about 2 minutes. Stir in the ginger and cook until fragrant, about 1 minute. Add the coconut milk and curry paste; bring to a simmer. Stir in the shrimp and 1/4 cup basil; simmer until the shrimp is opaque, about 3 minutes. Stir in the lime juice.
Divide the rice among bowls, top with the curry, garnish with remaining basil and serve with lime wedges.