Lime Shrimp with Coconut Rice

5 tablespoons unsalted butter
1 cup long-grain white rice
1 1/4 cups unsweetened coconut milk
1 lime
6 cloves garlic, minced
1 pound large shrimp, peeled and deveined
8 green onions, both white and green parts, thinly sliced
1/4 cup fresh cilantro

In a saucepan over medium heat, melt 1 tablespoon of the butter. Add the rice and cook, stirring constantly, until the grains are well coated with the butter, about 1 minute. Stir in 1 1/4 cups water and the coconut milk. Bring to a boil, reduce heat to low, cover, and cook until the liquid is absorbed and the rice is tender.
While the rice cooks, grate 1 teaspoon zest and squeeze 2 tablespoons juice from the lime. About 5 minutes before the rice is ready, in a large frying pan, over medium heat, melt the remaining 4 tablespoons butter. Add the garlic and lime zest and juice and stir until the mixture is bubbly. Add the shrimp and green onions and saute until the shrimp are opaque throughout, about 3 minutes. Stir in about half of the cilantro.
Fluff the rice and gently stir in the remaining cilantro. Top with the shrimp and serve.