In a small pot, simmer heavy cream, milk, sugar and salt until sugar completely dissolves, about 5 minutes.
Remove pot from heat.
In a separate bowl, whisk yolks.
Whisking constantly, slowly whisk about a third of the hot cream into the yolks, then whisk the yolk mixture back into the pot with the cream.
Return pot to medium-low heat and gently cook until mixture is thick enough to coat the back of a spoon (about 170 degrees on an instant-read thermometer).
Strain through a fine-mesh sieve into a bowl.
Whisk chocolate hazelnut spread and vanilla extract into base.
Cool mixture to room temperature.
Cover and chill at least 4 hours or overnight.
Churn in an ice cream machine according to manufacturers instructions.
Serve directly from the machine for soft serve, or store in freezer until needed.