Combine milk, cream, and 1/2 cup sugar in a saucepan over medium heat. Cook until sugar dissolves, about 5 minutes.

Beat egg yolks with the remaining sugar in a bowl with an electric mixer until eggs become thick and pale yellow, about 4 minutes.

Pour 1/2 cup warm milk mixture into egg mixture and stir. Add this mixture back into the saucepan. Cook over very low heat, stirring constantly, until the mixture becomes thick enough to coat the back of a wooden spoon, 7 to 10 minutes.

Place a strainer over a bowl and pour the warm custard mixture through the strainer. Stir in vanilla and hazelnut spread until it dissolves.

Chill mixture completely, about 1 hour. Pour into an ice cream maker and churn until frozen according to manufacturer’s instructions, 15 to 20 minutes.