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1
Bring milk, cream, and 1/2 cup sugar to a boil in a 3-quart heavy saucepan.
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2
Remove from heat, then stir in ginger and let steep, covered, 15 minutes.
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3
Meanwhile, whisk together yolks and remaining 1/2 cup sugar.
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4
Add milk mixture to yolk mixture in a slow stream, whisking, then transfer custard to saucepan.
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5
Cook over low heat, stirring constantly with a wooden spoon, until custard is thick enough to coat back of spoon and registers 175 to 180F on an instant-read thermometer (do not let boil).
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6
Pour custard through a fine-mesh sieve into a metal bowl, discarding solids, and chill, its surface covered with wax paper, until cold, about 1 1/2 hours.
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7
Freeze in ice cream maker, then transfer to an airtight container and put in freezer to harden, at least 4 hours.
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8
Bring cream and butter to a boil in a 1-quart saucepan.
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9
Pour hot cream over chocolate in a bowl and let stand 1 minute.
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10
Whisk ganache until smooth, then chill, covered, until firm, about 1 hour.
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11
Lightly brush 1 side of each of 6 wonton wrappers with beaten egg, then put 1 1/2 teaspoons chocolate ganache in center of each.
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12
Fold filled wontons in half to form triangles, pressing gently around filling to eliminate any air bubbles and sealing edges with more egg.
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13
(If there are any pockets of air, wontons may burst when fried.)
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14
Make 6 more wontons in same manner.
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15
Freeze filled wontons on a wax-paper-lined tray until firm, about 20 minutes.
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16
Heat oil in a 4-quart heavy saucepan over moderate heat until it registers 365F on deep-fat thermometer.
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17
Fry wontons, 3 at a time, turning once, until golden brown, about 1 1/2 minutes total.
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18
Transfer with a slotted spoon to paper towels to drain.
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19
(Return oil to 365F between batches.)
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20
Dust with confectioners sugar and serve wontons warm with ice cream.
