In a blender, blend coconut milk until smooth. Remove 1 ¼ cups coconut milk and pour into a small pot and set aside.

To the remaining ½ cup coconut milk in blender, add chopped pineapple, 3 tablespoons lime juice, garlic, 1 teaspoon salt, and ¼ teaspoon pepper. Blend until smooth. Pour into a large bowl and toss shrimp with marinade. Cover and chill.

Meanwhile, to the pot with coconut milk over medium heat, add rice, 1 ¼ cup water, and 1 teaspoon salt . Bring to a boil then reduce heat to low, cover, and simmer until rice is tender, 20 minutes. Remove from heat and keep warm.

In a large skillet over medium-high heat, heat 2 tablespoons oil. Drain shrimp and discard marinade. Add shrimp to skillet and season with salt and pepper. Cook, tossing occasionally, until just cooked through, about 5 minutes. Remove from heat and stir in cilantro.

In a medium bowl, toss cabbage with remaining 3 tablespoons lime juice, remaining 2 tablespoons oil, and salt and pepper.

Serve shrimp over rice with pineapple, cabbage, and lime wedges.