Bring milk to a simmer in a saucepan set over medium heat.
Whisk eggs in a large bowl until smooth. Whisk half of the hot milk into the eggs.
Pour egg and milk mixture back into the saucepan and cook over low heat, whisking constantly, until thickened into a custard, 3 to 4 minutes. Remove from heat; stir in white chocolate until melted. Stir in heavy cream and almond extract.
Refrigerate custard until thoroughly chilled, at least 1 hour.
Freeze in an ice cream maker according to manufacturer's instructions, 20 to 25 minutes. Transfer to a freezer-safe container and freeze until firm, 3 to 6 hours.