Add the milk and heavy cream to a medium saucepan. Warm over medium heat, stirring occasionally, until hot with small bubbles just starting to form around the edges, not boiling.
Meanwhile, whisk the egg yolks, sugar, and a pinch of salt together in a medium bowl until pale and well combined.
Slowly ladle about half a cup of the warm milk mixture into the egg yolks, whisking constantly. Repeat with another half cup, then pour the tempered egg mixture back into the saucepan with the rest of the milk and cream.
Return the saucepan to medium heat and cook, stirring constantly, until the custard thickens enough to coat the back of a spoon and holds a clean line when you run your finger through it, about 5 to 8 minutes. Do not let it boil.
Remove from the heat and stir in the vanilla extract.
Pour the custard into a bowl, cover, and refrigerate for at least 4 hours, or overnight, until completely cold.
Churn the chilled custard in your ice cream maker according to the manufacturer's instructions, until it reaches a soft-serve consistency.
Transfer to a freezer-safe container and freeze for at least 2 hours for a firmer scoop, or serve right away as soft serve.
