Freeze the bottom bowl of the ice cream maker for at least 24 hours before getting started.
In a saucepan, combine the chopped apricots, sugar, salt, and lemon juice. Cook over medium-low and stir frequently until the sugar dissolves. Continue to cook for 15-20 minutes, or until you have a syrup-like mixture, stirring once in a while to prevent burning. Keep an eye out to make sure the sugar does not start to caramelize, so it doesn't burn.
Allow the mixture to cool until safe to the touch. I do this by dunking the whole pan into a large bowl with ice and stirring every few minutes.
Use an immersion blender to carefully puree the apricot syrup until desired smoothness. The smoother the syrup, the smoother the ice cream. Or you can leave a few apricot chunks, that is also delicious! (See notes below for using a regular blender)
In a large bowl, combine the pureed syrup, heavy cream, half and half, milk, and vanilla extract and mix gently but thoroughly so that no syrup is sticking to the bottom.
Transfer into an ice cream maker and churn/process for 15-20 minutes. It's OK if it's not fully frozen after 20 minutes.
Carefully transfer to a freezer-safe dish (such as a loaf pan) and freeze for at least 4 hours, or until frozen.
Notes
I recommend keeping the ice cream maker bowl in the freezer all the time so it is always ready and fully frozen. Do not get started with a half-frozen ice cream maker bowl!
No immersion blender? Combine the apricot syrup mixture with the milk and puree in a blender until smooth. You don't want to puree only the syrup because a lot of it will stick to the blender and will be hard to scoop out.
If you don't have enough apricots, you can add some fresh or frozen peaches, nectarines, plums, or even mango.
Try saving a few tablespoons of the apricot puree to use as syrup for your ice cream!
To make really creamy ice cream: Make sure your ingredients are as cold as they can be straight from the fridge. This includes cooling the apricot syrup down so it's not hot.
Make apricot swirl ice cream: Save a little of the apricot syrup and swirl it in by the tablespoonful into the loaf pan right before freezing.
Scooping ice cream: Once frozen, the ice cream should be soft enough to be scoopable straight from the freezer, but if it is too hard, just let it sit at room temperature for 10-15 minutes before scooping.
Storing ice cream: Once the ice cream is frozen, cover it with food-safe plastic wrap or parchment paper, pressing gently into the top of the ice cream to remove any air.
Try adding a few pinches of cinnamon and a pinch of nutmeg to the apricot syrup for a subtle warmth from the spices.