Add sugar to a saucepan and cook over medium heat until melted and golden brown.
Pour the caramel into a baking dish or individual ramekins and spread evenly.
Dissolve instant coffee in a small amount of warm milk.
Whisk eggs, remaining milk, condensed milk, coffee mixture, vanilla extract, and salt until smooth.
Strain the custard mixture to create a silky texture.
Pour the coffee custard over the caramel and bake in a water bath until set but slightly jiggly in the center.
Cool completely, refrigerate for several hours, then invert onto a serving plate and serve chilled.