Whisk egg yolks, sugar, and salt together until mixture changes from dark golden to pale yellow becomes fluffy.
Heat milk and cream in a heavy saucepan over medium heat. Stir occasionally to prevent sticking to the bottom. Cook just until mixture starts to simmer when little bubbles begin to appear on the surface, 5 to 8 minutes. Remove from heat.
Whisk a ladleful of milk-cream mixture into the egg yolk mixture. Add another ladleful and whisk thoroughly before adding the next (this will keep the eggs from cooking). Gradually add the remaining milk-cream mixture and whisk thoroughly. Whisk in vanilla. Cool completely (you can place the bowl in a larger bowl with ice water to cool it faster).
Pour cooled mixture into a pitcher; cover. Refrigerate until ice cold or overnight.
Pour custard mixture into ice cream maker and process (according to manufacturer's instructions) until custard reaches the consistency of soft ice cream, about 20 minutes. Quickly transfer to a plastic container. Place a piece of plastic wrap over the surface of the custard. Cover container and freeze until custard is firm enough to scoop, at least 3 hours.