Vanilla Bean-Coconut Cupcakes with Coconut Frosting

Bring coconutmilk to boil in large deep saucepan overmedium-high heat (coconut milk will boilup high in pan). Reduce heat to mediumlow;boil until reduced to 1 1/2 cups, stirringoccasionally, 25 to 30 minutes.

Remove fromheat; cool completely.

Transfer to smallbowl. Cover; chill (coconut milk will settleslightly as it cools). DO AHEAD: Can be made2 days ahead. Keep chilled.

Position rack in centerof oven; preheat to 350°F. Line eighteen1/3-cup muffin cups with paper liners.

Whiskflour, baking powder, and salt in mediumbowl. Using electric mixer, beat butter inlarge bowl until smooth.

Add sugar; beat onmedium-high speed until well blended, about2 minutes.

Add 2 eggs, 1 at a time, beatingwell after each addition and occasionallyscraping down sides of bowl. Beat in seedsfrom vanilla bean and remaining egg.

Addhalf of flour mixture; mix on low speed justuntil blended.

Add 1 cup reduced coconutmilk; mix just until blended.

Add remainingflour mixture; mix on low speed just untilblended. Divide batter among muffin cups.

Bake cupcakes until tops spring backwhen gently touched and tester insertedinto center comes out clean, about 20minutes.

Transfer cupcakes in pans to rack;cool 10 minutes. Carefully remove cupcakesfrom pans and cool completely on rack.

Using electric mixer,beat butter in large bowl until smooth.

Add sugar, 1/3 cup reduced coconut milk,seeds from vanilla bean, and salt. Beat onmedium-low speed until blended, scrapingdown sides of bowl. Increase to mediumhighand beat until light and fluffy.

Using pastry bag fitted with large startip, pipe frosting onto cooled cupcakes.(Alternatively, top each cupcake with 2tablespoons frosting. Using small offsetspatula, swirl frosting over top of cupcakes,leaving 1/2-inch plain border.)

Sprinkle withcoconut. DO AHEAD: Can be made 1 dayahead. Store in airtight containers; chill.Bring to room temperature before serving.

* Available at many supermarkets and atIndian, Southeast Asian, and Latin markets.