Combine hot water and sugar in a bowl, stirring until the sugar completely dissolves. I always use fine sugar like King Arthur because it dissolves faster and creates a smoother syrup without any grittiness. Set aside to cool to room temperature—this prevents the syrup from cooking the apricots when combined and ensures a bright, fresh fruit flavor.
Blend the halved apricots and lemon juice together until completely smooth. Pour the mixture through a fine sieve into a bowl, pressing gently with the back of a spoon to extract as much liquid as possible while leaving behind any pulp and skins. Straining creates a silky-smooth sorbet base without any grainy texture or fibers.
Add the cooled simple syrup from Step 1 to the strained apricot purée from Step 2, then stir in the salt and vanilla extract. Salt enhances the apricot flavor and prevents the sorbet from tasting one-dimensional, while vanilla adds subtle depth. Cover and refrigerate for at least 1 hour until completely chilled—a cold base churns more efficiently and produces better texture.
Transfer the chilled mixture from Step 3 to your ice cream maker and churn according to the manufacturer's instructions, typically for 20-25 minutes, until it reaches a soft-serve consistency. Transfer to a freezer-safe container and freeze for at least 1 hour before serving. I find that letting it sit in the freezer overnight actually improves the texture, making it denser and creamier.