Add sugar, cornstarch, and salt to a large, heatproof glass bowl and stir with a whisk to combine.
Pour heavy cream and whole milk into a medium saucepan and heat to 150 degrees Fahrenheit.
Once heated, pour a splash of the hot milk and cream mixture into the sugar bowl and stir until smooth. Make sure no lumps of cornstarch are left behind.
Keep adding splashes of cream, pausing to stir in between, until there's about half of the cream left in the saucepan. The goal is to help the sugar/cornstarch mixture assimilate with the rest of the cream.
Pour the now smooth and thinned sugar and cream mixture into the saucepan with the rest. Turn the heat to medium low.
Stir continuously with a whisk until the mixture starts to gently rise and thicken. This should take anywhere from 3-5 minutes. Do not let it boil or the cream will curdle! :( The mixture is done when it resembles a thin pudding and a tail begins to form behind the whisk.
Immediately remove from heat and pour into a large glass heatproof bowl. Add 1 tbsp vanilla bean paste and 1 tsp vanilla extract and stir to combine.
Cover the bowl with plastic wrap, making sure to touch the cream with the plastic. This will prevent a skin from forming.
Place in the fridge for 8 hours or overnight until the cream is completely cold. (The longer it sits, the deeper the flavors will meld, and the creamier your ice cream will be.)
Once ready to churn, pour ice cream into your ice cream maker. This style of ice cream takes a lot less time to churn than traditional ice cream. I find it's usually done around 10 minutes. The cream should look thick with very large lumps. If using a kitchenaid mixer, it will be touching the attachment holding the churning device and have ice cream circling around the outer edges.
Stop the machine and immediately scoop ice cream into a quart-sized freezer container. It will have a soft-serve consistency until frozen. You will have some leftover for your immediate enjoyment. :)