How to Make It
Preheat oven to 375°F. Line a 15- x 10- x 1-inch jelly roll pan with parchment paper, folding creases firmly so paper lies against edges of pan and has some overhang. Coat parchment with cooking spray. Cut another large sheet of parchment paper, and set aside on a work surface.
Place eggs in the bowl of a stand mixer; beat at medium-high speed with paddle attachment until slightly thickened, about 4 minutes. Beating at high speed, gradually add granulated sugar; beat until pale and slightly thick, about 3 minutes. Add coconut water and 1 teaspoon vanilla; beat at low speed just until combined.
Whisk together flour, baking powder, and salt in a bowl. Add flour mixture to egg mixture; beat at low speed until well combined. (Batter will be thin.) Pour batter into prepared pan, spreading to edges. Bake in preheated oven until cake springs back when lightly touched in center, 12 to 14 minutes. (Surface of cake will look porous.) Meanwhile, clean bowl of stand mixer.
Working quickly, remove cake from pan by holding onto parchment paper. Invert onto sheet of parchment paper on work surface; peel off and discard parchment from cake. Quickly turn cake over so porous side is facing up. Poke holes all over surface of hot cake with a fork; spread sweetened condensed coconut milk evenly over cake. Starting with one of the short sides, roll up the cake tightly but gently in the parchment paper. Let cool on a wire rack, seam side down, until completely cool, about 1 hour.
Place heavy cream and 3 tablespoons powdered sugar in cleaned bowl of stand mixer; beat with whisk attachment at high speed until stiff, firm peaks form. Carefully unroll cake (it will be sticky), gently prying with fingers if it sticks to paper. Spread whipped cream evenly over entire surface of cake. Reroll cake; arrange on a platter, seam side down. Place in refrigerator.
Scoop out 1/2 cup solidified coconut cream, and place in bowl of stand mixer (no need to rinse it out); reserve remaining coconut cream and liquid for another use. Add butter to bowl; beat with cleaned paddle attachment at medium speed until well combined, about 1 minute. (It’s OK if it clumps up slightly.) Add remaining 2 1/2 cups powdered sugar; beat at low speed, increasing speed to medium-low, until smooth and creamy. Beat in remaining 1/2 teaspoon vanilla. Spread frosting evenly over top, sides, and ends of cake. Gently press coconut chips into frosting. Serve immediately, or chill until ready to serve.