Step 1

Whisk together egg yolks and 1/2 cup of the brown sugar in a medium bowl; set aside. Stir together milk, whipping cream, and remaining 1/2 cup brown sugar in a medium saucepan until smooth. Cook over medium, stirring occasionally, until mixture is hot but not boiling, about 4 minutes. Gradually pour 1 cup hot milk mixture into egg yolk mixture, whisking constantly. Gradually whisk egg yolk mixture into remaining hot milk mixture in saucepan. Cook over medium, stirring constantly, until mixture coats back of a spoon, about 4 minutes. Remove from heat; stir in salt and vanilla. Pour mixture into a large bowl; place bowl inside a larger bowl filled with ice water, and let mixture cool to room temperature, about 30 minutes. Transfer mixture in bowl to refrigerator; chill until cold, about 2 hours.

Step 2

Pour chilled mixture into frozen freezer bowl of a 4-quart electric ice-cream maker, and proceed according to manufacturer's instructions. (Instructions and times may vary.) Transfer to an airtight freezer-safe container; freeze until firm, about 4 hours. Sprinkle with additional salt, and serve.