Make batter: Preheat oven to 350º (we used our Krups toaster oven for this recipe). In a medium mixing bowl, combine coconut cream (the thick white cream inside the can), coconut milk (liquid from same can) and sugar. Beat with a hand mixer until smooth.
Add vegetable oil and egg to bowl and beat gently until combined. Mix in flour, baking powder, and salt until combined, then gently mix in pineapple purée.
Spoon into mini muffin cups and fill until three-fourths full. Bake until a toothpick comes out clean, 12 to 15 minutes.
Make frosting: Place white chocolate in a medium bowl. In a microwave, heat pineapple juice until scalding hot, 30 to 45 seconds. Pour juice over chocolate and place a plate on top to keep warm. Let sit 5 minutes, then whisk until smooth. Let thicken, 10 minutes.
Once frosting has thickened, dip tops of cupcakes into frosting. Garnish with coconut and lime zest.