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1
Bring cream, milk, sugar, and salt to a boil in a 2-quart heavy saucepan, stirring until sugar is dissolved.
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2
Whisk eggs in a bowl until blended, then add hot cream mixture in a slow stream, whisking.
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3
Transfer custard back to saucepan and cook over moderately low heat, stirring constantly with a wooden spoon, until thick enough to coat back of spoon and registers 175 to 180F on thermometer (do not let boil).
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4
Immediately pour through a fine-mesh sieve into cleaned bowl, then stir in liqueur.
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5
Cool custard to room temperature, stirring occasionally, then chill, its surface covered with a round of wax paper, until cold, about 3 hours.
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6
Preheat oven to 350F.
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7
Line bottom of square baking pan with wax or parchment paper.
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8
Melt chocolate with water in a small heavy saucepan over very low heat, stirring, then cool to lukewarm.
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9
Beat yolks, 1/3 cup sugar, and salt in a large bowl with an electric mixer at high speed until thick and pale, about 5 minutes in a standing mixer or about 8 minutes with a handheld.
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10
Fold in melted chocolate.
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11
Beat egg whites with cleaned beaters until they hold soft peaks.
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12
Beat in remaining 1/3 cup sugar 1 tablespoon at a time and continue to beat until whites just hold stiff peaks, about 5 minutes.
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13
Fold one third of whites into chocolate mixture to lighten, then fold in remaining whites gently but thoroughly.
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14
Spread batter evenly in baking pan and bake in middle of oven until puffed and a wooden pick or skewer inserted in center comes out with crumbs adhering, 30 to 35 minutes.
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15
Transfer pan to a rack, then cover top of cake with 2 layers of dampened paper towels and let stand 5 minutes.
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16
Remove towels and cool cake completely in pan (cake will deflate as it cools).
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17
Sift 1 1/2 tablespoons cocoa over cake, then loosen edges with a sharp knife.
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18
Invert a wax-paper-lined baking sheet over cake and invert cake onto it, then gently peel off wax paper now on top.
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19
Freeze custard in ice cream maker.
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20
Transfer ice cream to an airtight container and freeze until firm but still spreadable, about 30 minutes.
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21
Oil milk carton, then line bottom and long sides with a sheet of plastic wrap, leaving at least a 2-inch overhang.
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22
Trim cake to form a 7 1/2- by 6 1/4-inch rectangle (reserve trimmings for another use), then cut rectangle lengthwise into 5 (7 1/2- by 1 1/4-inch) strips.
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23
Using thin metal spatula, arrange 2 strips on bottom of carton, flush against each long side.
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24
Fill space between strips with ice cream (preferably using a small offset metal spatula).
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25
Arrange 1 cake strip down center of carton (on top of ice cream) and fill spaces on both sides of cake with ice cream.
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26
Arrange remaining 2 cake strips against long sides of carton (on top of ice cream) and fill space between them with ice cream.
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27
(There will be some leftover ice cream.)
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28
If ice cream becomes too soft during assembly, freeze until just firm enough to work with, about 15 minutes.
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29
Cover top with plastic wrap overhang, then freeze until dessert is hardened, at least 8 hours.
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30
To serve, unwrap overhang and invert carton onto a chilled platter, using plastic wrap to help pull cake from carton.
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31
Trim sides evenly to neaten loaf if necessary (ice cream may ooze a bit on sides), then sift remaining 1 1/2 tablespoons cocoa over top.
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32
Cut into slices with a sharp knife.
