Place butter, honey, and salt in a small saucepan. Bring to a boil over medium-high heat, and stir occasionally until caramel is a deep golden brown and slightly thickened. Remove from heat and whisk in cream. Set aside.
Assemble the affogato: Place scoops of ice cream in a serving bowl. Drizzle warm caramel sauce over ice cream and pour espresso over top. Enjoy ice cream immediately!