In a medium pot over medium heat, add the Yakult. Simmer the Yakult until it reduces enough that it measures 1 cup (you can check by transferring to a heatproof liquid measuring cup), scraping the pot occasionally to limit the Yakult from burning (but no worries if it burns a little, since they will be strained out). It should take about 20-25 minutes.
Once the Yakult has reduced, add the cream, sugar and salt. Simmer until the sugar completely dissolves, about 5 minutes. Remove pot from heat. In a separate bowl, whisk the yolks until they're broken up.
Whisking constantly, slowly whisk about a third of the hot mixture into the yolks, then whisk the yolk mixture back into the pot with the cream. Return the pot to medium-low heat and gently cook until the custard is thick enough to coat the back of a spoon or spatula.
Cool the custard to room temperature. Strain through a fine-mesh sieve into a bowl and discard any scrambled egg or burn bits that get caught in the sieve. Stir in the vodka.
Cover and chill at least 8 hours or overnight. If the custard separates while it’s chilling, mix it back together and it’ll be good as new.
Churn in an ice cream machine according to manufacturers’ instructions; it'll look like thick whipped cream when it's done. Transfer the ice cream to a container (I like to use a long, shallow container because it helps me get better scoops than a pint container), smooth the top and cover. Freeze until solid.
Recipe Notes
Don’t worry if the Yakult burns a little bit, since you will strain these bits out later. You might be tempted to skip this straining step, but it is necessary for this recipe.
You can omit the alcohol if you’d like. It’s mostly for texture (and not for flavor), and the ice cream is easy to scoop straight from the freezer, but the ice cream will still be tasty if you decide not to use it.