Prepare a large bowl or pan of ice water.

In the top of a double boiler, heat the half-and-half over simmering water until steaming.

In a bowl, whisk the egg yolks until blended, then whisk in the sugar. Whisk in about half of the hot half-and-half and pour the yolk mixture into the pan of half-and-half.

Stir with a silicone spatula or spoon and cook over simmering water for about 8 minutes.

Stir in 1 cup of the chips and continue stirring until blended in and the custard coats the back of the spatula, about 2 minutes more.

Immediately place the custard pan in the ice bath and stir the custard occasionally until it cools to room temperature. Transfer to a container and stir in the cream and vanilla.

Cover and refrigerate until thoroughly chilled, about 3 hours.

Freeze in an ice cream maker according to the manufacturer’s instructions.

When the ice cream is almost frozen, add the remaining 1 cup chips and churn until blended in, about 15 seconds more.

Transfer to a container, cover, and freeze until firm, about 2 hours.