Combine 1/4 cup (50 grams) of the sugar with the water in a small saucepan. Place over medium-high heat and bring to a boil, stirring frequently, about 3 minutes. Stir in the pectin and return to a full rolling boil, then continue stirring at a boil for exactly 1 minute. Remove from the heat and leave at room temperature to cool, about 25 minutes. Temperature should land around 89 degrees F.
While the pectin mixture cools, combine the remaining 1/2 cup (100 grams) of the sugar with the half and half, cream, 1 tablespoon (20 grams) of the vanilla bean paste, and the salt in a medium saucepan. Place over medium heat and, stirring frequently, bring the mixture to 185 F, 5 to 7 minutes. Remove from the heat, cover, and steep for 20 minutes.
Thoroughly stir the cooled pectin mixture into the cream along with the remaining 1 tablespoon (20 grams) of the vanilla bean paste. Set the pan inside a bowl of ice and stir to cool down the mixture to room temp. Transfer to an airtight container and refrigerate for at least 6 hours or up to 24 hours.
Assemble your ice cream maker according to manufacturer's instructions. Turn the machine on, and pour the ice cream mixture in.
Churn the ice cream until it reaches soft-serve consistency, 20-30 minutes, depending on the ice cream maker. Quickly transfer to 3 pint size containers and freeze until scoopable, at least 4 hours, before serving.