Whisk together sugar, cornstarch, and salt in a saucepan.
Slowly pour in the milk, whisking until smooth.
Heat over medium, stirring constantly, until the mixture thickens slightly and coats the back of a spoon.
Remove from heat and stir in honey and vanilla.
Add the optional alcohol if using.
Cool completely, then chill in the fridge until very cold.
Pour into a shallow dish and freeze for 45 minutes.
Scrape the edges and stir or whisk vigorously to break up ice crystals.
Repeat every 30 minutes for 2–3 hours.
Once creamy and thick, transfer to a container and freeze 2 hours to set.