For sauce: Whisk yolks and sugar in large bowl to blend; bring milk just to simmer in medium saucepan; gradually whisk hot milk into egg mixture; return mixture to same saucepan and stir over medium-low heat until sauce thickens and coats back of spoon, about 7 minutes (do not boil); pour into bowl; stir in vanilla; place plastic wrap directly onto surface of custard and cool; cover and refrigerate until cold.
For Baked Alaskas: Preheat oven to 350°F; butter and flour 10 ½ x 15 ½ x 1-inch jelly roll pan; sift first 5 ingredients into large bowl; repeat sifting; combine water and espresso powder in large bowl and stir to dissolve; add buttermilk, oil and eggs and whisk to combine; add to dry ingredients and whisk until blended; pour batter into prepared pan; bake until tester inserted into middle of cake comes out clean, about 30 minutes; transfer to rack and cool completely (Sauce and cake can be prepared 1 day ahead; cover cake and refrigerate).
Using 4-inch-diameter round as guide, cut out 1 cake round; slide metal spatual under cake round and transfer to baking sheet; repeat, forming 5 more cake rounds; reserve remaining cake for another use; place rounded scoop of ice cream on top of each cake round; freeze, uncovered, for up to 8 hours.
Using electric mixer, beat egg whites in large bowl until soft peaks form; gradually add 1 ½ cups sugar and beat mixture until stiff and glossy.
Spoon meringue into pastry bag fitted with medium star tip; pipe meringue in star shapes on top of ice cream, covering ice cream completely, but leaving cake visible underneath (ice cream should be completely encased in meringue, with a seal where ice cream meets cake); freeze until ready to bake (Can be prepared 1 day ahead).
Preheat oven to 500°F; bake desserts until meringue is light brown, about 2 minutes; using spatula, transfer each Baked Alaska to individual plates; spoon sauce onto plates and serve immediately.