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1.
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To make the drunken fig filling: Put all the ingredients into a large mixing bowl and stir well to coat the figs with the sugar.
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Cover and set aside at room temperature for at least 30 minutes, or as long as overnight.
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2.
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Transfer the figs and liquid to the bowl of a food processor or an electric mixer fitted with the paddle attachment.
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Process or beat the mixture until mashed to a paste.
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(You can also mash the mixture by hand with a fork.)
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Cover and refrigerate until ready to use; the filling can be kept for up to 2 weeks.
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3.
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To make the sesame balls: Put the sugar, salt, and baking soda into the bowl of an electric mixer fitted with the paddle attachment and mix well; set aside.
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4.
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Fill a large saucepan fitted with a steamer basket or rack with water to a dept of 2 inches and bring to a rolling boil.
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Put the taro in the basket and steam until very soft, about 10 minutes; it should fall apart if poked with a knife.
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Immediately add the taro to the sugar mixture, and beat on medium speed until smooth and pasty, about 5 minutes.
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5.
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Meanwhile, bring 1 cup plus 2 tablespoons water to boil.
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6.
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Turn the mixer speed to low and add the glutinous rice flour.
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When the mixture is crumbly, add the boiling water all at once.
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(The water must be boiling when added.)
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Continue beating until the dough is soft and only slightly sticky.
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Squeeze the dough into a ball, wrap in plastic wrap, and set aside until it cools to room temperature.
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7.
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Shape the dough into a log 1 inch in diameter, and cut the log into 2-inch lengths.
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One at a time, flatten each piece of dough with your palm into a circle 4 inches in diameter and 1/4 inch thick.
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Put 1 tablespoon of the chilled fig filling into the center of the circle, then bring the edges together to form a half-moon and pinch to seal.
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Pinch off the excess dough at the two ends and roll the filled dumpling into a ball.
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Set aside.
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8.
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Fill a deep, heavy saucepan with oil to depth of at least 3 inches and heat to 300F.
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Fill a shallow dish with 1/8 inch of water and another shallow dish with the sesame seeds.
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Roll a sesame ball in the water, just enough to moisten, then roll in the sesame seeds until well coated.
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Press the seeds so they stick to the balls, if necessary.
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Carefully lower the coated ball into the oil and cook, without stirring, until it floats and is crisp and light golden brown, about 5 minutes.
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You can cook about 8 balls at a time, but do not overcrowd the pan.
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Carefully remove from the oil and drain on paper towels.
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Repeat with the remaining balls.
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Serve hot or at room temperature.
