Swirl Scotch, sugar and salt in a medium heavy saucepan to combine. Heat on medium-high for 30 seconds, you should start to smell the alcohol vapor; using a stick lighter or long match, ignite the alcohol. Continue cooking, flames will be small at first and grow as the mixture heats but will die out completely after about 2 minutes.
Boil sugar mixture, swirling occasionally (do not stir or crystals may form and result in a grainy caramel), until the edges start to turn golden, about 7-9 minutes. Keep swirling to mix the lighter and darker colors until the caramel is amber, another 2–3 minutes. Watch closely because the caramel can darken and burn quickly.
As soon as it reaches amber, remove from heat, add butter and continue to swirl to melt the butter and to stop the caramel from getting any darker; butter will make the caramel bubble vigorously so be careful. When the butter is completely melted, swirl in heavy cream. Stir (it’s ok to stir at this point) until cream is completely incorporated and caramel is smooth and no streaks of cream remain. Let cool, caramel will thicken as it sits.
Divide ice cream among 12 highball glasses or bowls. Pour 1/2 shot of espresso over each and top with a drizzle of caramel.
Do ahead: Caramel can be made 1 month ahead, store in an airtight container and chill. Reheat gently before using.