1Let butter and eggs stand at room temperature for 30 minutes. Grease and flour a 10-inch tube pan; set aside.
2In a large bowl, beat the butter, baking powder and salt with an electric mixer on high speed for 30 seconds. Gradually mix in 1-1/2 cups sugar, a little at a time, beating until well combined. Scrape the sides of the bowl and beat for 2 more minutes.
3Add 3 eggs, one at a time, beating well after each. Beat in 1 tsp. vanilla.
4In a small bowl, combine the milk, cream of coconut, lime zest and lime juice. Alternately add milk mixture and flour mixture to butter mixture, beating on low speed after each addition, until just combined.
5Spread the batter evenly in the prepared tube pan. Bake in a preheated 350-degree oven for 40 minutes or until a toothpick inserted near the center of cake comes out clean. Cool in pan on a wire rack for 15 minutes. Remove from pan and cool further on a wire rack.
6FOR MERINGUE FROSTING:
In the top of a double boiler, combine 1-1/2 cups sugar, the water, two egg whites and the cream of tartar. Beat with an electric mixer on low for 30 seconds. Place over the boiling water in the double-boiler and cook, beating constantly on high speed, about 7 minutes or until stiff peaks form, scraping pan constantly.
7Remove from heat and add 1 tsp. vanilla. Beat 2 to 3 minutes more or until frosting reaches spreading consistency.
8Frost the cake and sprinkle with coconut chips and lime slices. Serve soon after frosting.
9NOTE: After the cake has come from the oven and has cooled, it can be stored, unfrosted, in an airtight container at room temperature for up to two days.