Mix and heat half the cream (1c, 240ml, or 245g), the milk, sugar, and salt in a saucepan until all of the sugar has dissolved. Whisk in the vanilla bean paste, turn off the heat, and let the mixture sit until its temperature comes down to 140℉ (60℃).
In a separate bowl, whisk the eggs yolks until they froth and lighten in color slightly. Then, slowly temper the cream mixture into the egg yolks by gradually adding small amounts of cream to the eggs, whisking constantly, until all of the cream mixture is combined.
Add the remaining cup of cream to a large bowl, place a fine mesh strainer on top, and set it aside.
Scrape the fully combined mixture back into the saucepan and stir it constantly over medium-low heat with a heatproof spatula until mixture thickens and coats the spatula. Make sure to check the temperature while you heat the creme anglaise. The optimal temperature for thickening is 180℉ (82℃). I tend to keep mine between 170-175℉ (76-79℃) to be on the safe side.
If you are really worried about overcooking the creme anglaise, you can always use a double boiler as a safety net. You'll know it is done when you can run your finger across the coated spatula and the creme anglaise doesn't run back together. (see notes)
Now, pour the thickened custard through the strainer and into the bowl of chilled cream. Stir the custard and cream together and add in the vanilla extract, to complete the ice cream base. Then, chill the mixture completely in the refrigerator. It should take roughly 4-8 hours.
When ready to churn, pour the vanilla ice cream base into an ice cream maker and freeze according to the manufacturer's instructions. Once done, scrape the ice cream out of the mixer and into a freezer safe container. Freeze the semi-frozen ice cream for at least another 4 hours or overnight for best results.