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1
Preheat oven to 375 deg F. Lightly grease a large baking sheet or line with parchment paper.
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2
Put the butter, water, milk and salt in a medium saucepan, and heat until the butter has melted and the mixture has come to a full boil. In the meantime, put the tapioca starch in the bowl of your stand mixer.
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3
Pour the boiling mixture over the tapioca starch, beating to combine. Continue beating at a high speed until the mixture becomes smooth and elastic-looking - this will take only a couple of minutes.
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4
Beat in the garlic and cheese until well combined.
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5
Stick your finger into the dough. If it's uncomfortably hot, wait until it cools a bit. It should still be rather hot, but not uncomfortable.
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6
With the mixer going, gradually dribble in the beaten eggs, beating till well combined and smooth.
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7
Drop the mixture in 2 tbl balls (about the size of a golfball) onto the baking sheet, spacing about 1 1/2 in apart. Don't worry if the surface is a little rough - it will smooth out as it rises and bakes. The balls will flatten a little, but should hold their shape.
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8
Bake the rolls for about 20 minutes, until they have a freckled appearance (from the browning cheese) and begin to color a bit.
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9
Remove from oven and serve hot. Reheat briefly in the microwave if serving at a later time.
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10
Note: KA mentioned that tapioca starch or flour varies from brand to brand and even from batch to batch. You may need to add more tapioca, up to about 1/2 cup, to get a good consistency dough. If you've ever made cream puffs, that's the consistency you are looking for.