Whisk together sugar, eggs, and egg yolk in a medium bowl until lighter in color.

In a saucepan over medium heat, bring the half-and-half and whipping cream to 160°F. Remove from the heat. Use a ladle to add a little of the cream to the eggs/sugar and whisk to combine. Continue adding cream until at least half has been mixed with the eggs.

Add the eggs/cream mixture back to the pan and whisk to combine.

Over medium heat, cook the mixture until it reaches 170 to 175°F, stirring constantly.

Pour mixture into a medium bowl. Add vanilla and peanut butter and whisk to combine until smooth.

Cover mixture directly on top with plastic wrap to prevent a skin from forming. Cool to room temperature then chill overnight.

Pour chilled mixture into an ice cream maker and freeze according to the manufacturer's instructions.

Stir in chocolate chips.

Transfer ice cream to a freezer safe container and freeze for at least one hour or overnight.