Bring milk and vanilla to a boil in a medium saucepan. Remove from heat. Whisk about one-third of the liquid into yolk mixture. Pour mixture back into pan with remaining custard; whisk to combine. Cook over medium heat, stirring constantly, until mixture registers 185 degrees on an instant-read thermometer. Remove from heat; strain. Refrigerate until cool.

Put butter into the bowl of an electric mixer fitted with the paddle attachment; mix on medium-high speed until pale and fluffy. Mix in chilled custard.

Heat egg whites and remaining 1 cup sugar in the clean heatproof bowl of an electric mixer set over a pan of simmering water, whisking constantly, until sugar has dissolved. Attach bowl to mixer fitted with the whisk attachment; beat on high speed until stiff peaks form.