Place an 8x8 or 9x9 pan square metal baking pan in the freezer.
Combine vanilla bean paste, heavy cream, whole milk, 6 Tablespoons sugar, corn syrup, and salt in medium saucepan. Heat over medium high heat, stirring occasionally, until mixture is steaming steadily and registers 175oF degrees, 5 to 10 minutes. Remove saucepan from heat.
While cream mixture heats, whisk remaining 1/4 cup sugar and egg yolks in a bowl until smooth, about 30 seconds.
Slowly whisk 1 cup of the heated cream mixture into the egg yolk mixture. Then pour the egg yolk mixture into the saucepan and cook over medium low heat, stirring constantly until mixture thickens and registers 180oF (about 7 to 14 minutes).
Immediately pour custard into large bowl and let cool until no longer steaming, 10 to 20 minutes. Transfer 1 cup of the custard to a small bowl. Cover both bowls with plastic wrap. Place large bowl in the refrigerator and the small bowl in the freezer and let cool completely at least 4 hours or up to 24 hours. (The small bowl will freeze solid)
Remove custards from refrigerator and freezer. Scrape frozen custard from small bowl into large bowl of custard. Stir occasionally until frozen custard through fine mesh strainer and transfer to ice-cream machine. Churn until the mixture resembles soft serve ice cream and registers 21oF (about 25 minutes).
Transfer icecream to to frozen baking pan and press plastic wrap on the surface. Return to freezer until firm around the edges, about 1 hour.
Transfer icecream to airtight container, press firmly to remove any air pockets and freeze firm at least 2 hours (ice cream can be frozen for up to 5 days)