Whisk together 1/4 cup (59 ml) of the cream with the egg yolks.
3 large egg yolks
Pour the remaining 1 1/4 cups (295 ml) heavy cream into a large mixing bowl. Set a fine-mesh sieve over the mixing bowl.
Melt the butter in a medium saucepan over medium heat.
1/4 cup (56 grams) unsalted butter
Add the brown sugar, granulated sugar, and salt. Cook, stirring constantly, until the butter and sugars are hot and thoroughly combined. It might look like the butter isn’t combining with the sugar at the beginning, but the mixture will come together as it warms up. The mixture should be cohesive and bubbling, but do not continue cooking if it becomes dry or crumbly (after the liquid, runny stage). That happened with my first batch. If that happens to you, you can go on to the next step and let it slowly dissolve in the milk.
1/2 cup + 2 tablespoons (125 grams) light brown sugar, packed, 2 tablespoons (25 grams) granulated sugar, 1/2 teaspoon fine salt
Remove the saucepan from the heat and slowly whisk in the milk. The mixture may bubble vigorously at first. Return the saucepan to the heat and cook until the mixture is hot and steaming.
1 cup (236 ml) whole milk
Slowly pour about 1 cup of the hot butterscotch mixture into the egg yolk mixture in a thin, steady stream, whisking constantly.
Cook over medium-low heat, stirring constantly, until the custard reaches 170-175 °F (77-79 °C). Do not let it boil.
Pour the hot custard through the fine-mesh strainer directly over the cold cream. Stir in the vanilla extract.
1 1/2 teaspoons vanilla extract
If using an ice cream maker, you can cover the mixing bowl and refrigerate until completely cold, about 4 hours but preferably overnight (the colder it is, the better it'll churn). If making the no-churn version, transfer the mixture to a freezer-safe container that will fit in your freezer. Refrigerate the custard until it's completely cold, about 4 hours.
For the churned option: churn the chilled custard in an ice cream maker according to the manufacturer's instructions. Transfer to a freezer-safe container and freeze until firm enough to scoop, about 4-8 hours.
For the no-churn option: transfer the custard to the freezer and freeze for about 8 hours or until solid enough to scoop.
Freeze for up to 3 months. For the best texture, press a piece of parchment paper or plastic wrap directly against the surface before putting the lid on.