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In a small saucepan bring the pineapple juice to a boil. Continue to boil until the juice has reduced to ½ cup.
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Let juice cool while you make the sponge.
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To make the sponge, mix ¼ cup of the all-purpose flour, 1/3 cup lukewarm water and the tablespoon of the yeast in the bowl of a mixer.
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Combine well and let sit for 20 minutes. The sponge should start to puff up and look spongy.
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Add the remaining flour, the vanilla, butter, eggs, brown sugar, and the salt.
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With a dough hook knead the dough for 6 to 8 minutes. The dough should get smooth but will not pull all the way away from the sides of the bowl.
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Lightly grease a 4-5 cup bowl. Scrape the dough into the greased bowl and cover.
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Let rise for an hour or a bit more depending on the temperature of your kitchen, until the dough has more than doubled but not tripled.
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Lightly grease a 13 x 9 baking pan.
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On a lightly floured work surface and with floured hands divide the dough into 16 equal pieces. The dough will be a bit sticky. Roll each portion into a smooth ball and place into evenly into the prepared pan. I did offset rows of four.
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Brush the rolls with a beaten egg as an egg wash.
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Let the rolls rise for one hour or until very puffy and nearly doubled.
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While the rolls are rising, preheat the oven to 350°.
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Brush the rolls again before you put them into the oven
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When the rolls have risen, bake them for 20 to 25 minutes or until nicely golden brown.
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Let the rolls cool in the pan for 1a few minutes and then turn out onto a cooling rack.
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You can serve these rolls warm or let cool completely and store well wrapped for several days.