Heat the half and half, cream, vanilla bean paste, 1/2 cup of the sugar, and salt in a 2-quart pot over medium heat. Cook, stirring frequently, until the temperature reaches 185℉, about 5 minutes. Kill the heat and cover the pot with a lid.
Combine the remaining 1/4 cup of sugar, water, and pectin in a 1-quart pot over medium-high heat and bring to a boil. Boil for exactly 1 minute, remove from heat and whisk into the dairy mixture until fully combined.
Fill a large bowl with ice and water to come half way up the sides of the bowl. Place a medium bowl directly over the ice water then pour the ice cream mixture in. Whisk frequently until the mixture comes to room temperature.
Pour the ice cream base into a 1-quart size container and cover tightly. Refrigerate until the temperature drops below 40℉, at least 4 hours or overnight.
Pour the mixture into a prepped ice cream maker and process according to the manufacturer's directions. You'll know it's ready when you hear the motor begin to struggle a bit and the ice cream becomes very thick, approximately 20-30 minutes. Serve as is for soft serve or freeze for another 3-4 hours to allow the ice cream to harden.