Heat the evaporated milk in a 2-quart saucepan over low heat until warm.
Stir together the sugar and 2 tablespoons of the espresso in a heavy saucepan. Place over high heat and cook, without stirring, about 2 minutes (the mixture will bubble), until the sugar has caramelized to a dark amber. Remove from the heat and pour in the remaining 2 tablespoons espresso.
Stir the espresso mixture into the warm milk and mix well. Stir in the vanilla and salt. Cover and chill thoroughly.
Freeze in an ice cream maker according to the manufacturer's directions.