Instructions

MAKE THE ENRICHED BUN DOUGH:
In a large bowl or stand mixer combine flour, sugar, yeast and salt.
In a separate bowl whisk together warm milk, coconut milk and eggs.
Add wet ingredients to dry ingredients. Mix on low speed until combined then knead on medium speed for 8-10 minutes or by hand for 12-15 minutes until smooth and elastic.
Add softened butter and vanilla. Continue kneading until butter is fully incorporated and dough is silky (about 5 more minutes).
Place dough in greased bowl. Cover with plastic wrap and let rise in warm place until doubled - about 1-1.5 hours.

SHAPE THE BUNS:
Line two baking sheets with parchment paper. Punch down dough and turn out onto lightly floured surface.
Divide dough into 12 equal pieces about 75g each. Roll each piece into a finger shape about 5-6 inches long.
Place shaped buns on prepared baking sheets spacing 2 inches apart. Cover loosely with oiled plastic wrap.
Let rise until puffy and nearly doubled 45-60 minutes.

MAKE THE PINEAPPLE GEL:
While dough rises combine pineapple, sugar and lime juice in a saucepan. Cook over medium heat until pineapple softens about 8-10 minutes.
Stir in cornstarch mixture and cook stirring constantly until thickened and glossy about 2 minutes.
Remove from heat add pinch of salt. Transfer to bowl and cool completely. Refrigerate until ready to use.

MAKE THE COCONUT CRÈME PÂTISSIÈRE:
In a saucepan heat coconut milk over medium heat until steaming. Do not boil.
In a bowl whisk together sugar, egg yolks and cornstarch until smooth and pale.
Slowly pour hot coconut milk into egg mixture whisking constantly to temper.
Return mixture to saucepan. Cook over medium heat whisking constantly until thick and bubbling about 3-5 minutes.
Remove from heat. Whisk in butter, vanilla and toasted coconut. Press plastic wrap directly onto surface and refrigerate until cold at least 2 hours.

BAKE THE BUNS:
Preheat oven to 375°F. Brush risen buns gently with milk.
Bake 18-20 minutes until golden brown and internal temperature reaches 190°F.
Transfer to wire rack and cool completely.

MAKE THE RUM ICING:
In a bowl whisk together powdered sugar, 2 tablespoons rum, 2 tablespoons coconut milk and vanilla until smooth. Add more liquid if needed for spreadable consistency.
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ASSEMBLE THE BUNS:
Using a sharp knife cut a slit lengthwise down the center of each cooled bun cutting about 2/3 through.
Pipe or spoon pineapple gel into the bottom of each slit.
Pipe or spoon coconut crème pâtissière on top of pineapple gel filling generously.
Spread rum icing over the top of each bun. Sprinkle with toasted coconut flakes.
Let icing set for 15 minutes before serving.