Add sugar to a saucepan and cook over medium heat until it melts and turns golden brown.
Pour the caramel into a baking dish or individual ramekins and spread evenly.
In a bowl, whisk eggs, milk, sugar, and vanilla extract until well combined.
Strain the custard mixture to remove any lumps and create a smooth texture.
Pour the custard gently over the cooled caramel.
Place the dish in a water bath and bake until the custard is set but still slightly jiggly in the center.
Cool completely, refrigerate for several hours, then invert onto a serving plate and serve chilled.