In a medium saucepan set over medium heat, combine the half and half, 1 c. of heavy cream, granulated sugar, corn syrup, and salt.
Heat until warm (if using vanilla beans, you'll want to add the scraped seeds, whisk in, cover and steep/sit for 30 minutes, re-warm the mixture and continue as follows).
In a small mixing bowl whisk together the eggs, slowly pour the warm mixture into the eggs, whisking constantly. Go really slow so you don't scramble them! Gradually pour the mixture back into the saucepan. Constantly whisk over medium heat until the mixture thickens and reaches a temperature of 165 degrees.
Pour the mixture through a mesh sieve set over a medium size mixing bowl. Stir in the remaining heavy cream and the vanilla bean paste. Once this is done, I generally set my bowl over an ice bath to cool the base down as quickly as possible.
Cover and refrigerate for at least 2 hours, preferably overnight.
Remove the ice cream base from the refrigerator and pour into a prepared ice cream machine or attachment bowl. Freeze according to the manufacturer's instructions (about 25 minutes).
When the ice cream is firm, place in a freezer-safe container. Freeze for 2-4 hours before serving.