Make the caramel: Heat sugar and water in a saucepan over medium heat, swirling occasionally, until it turns deep amber.
Pour the hot caramel into ramekins or a baking dish, tilting to coat the bottom evenly. Let it harden.
Heat milk, cream, and espresso in another saucepan over medium heat until warm but not boiling.
In a separate bowl, whisk eggs, yolks, and sugar until smooth.
Slowly pour the warm coffee mixture into the eggs, whisking constantly to avoid scrambling.
Stir in vanilla extract and strain through a fine-mesh sieve to ensure smoothness.
Pour the mixture into prepared ramekins.
Place the ramekins in a baking pan and pour in hot water, reaching halfway up the sides.
Bake at 325°F (163°C) for 50 minutes, or until the center is just set but slightly jiggly.
Let cool, then refrigerate for at least 3 hours.
Run a knife around the edges and invert onto a plate. Enjoy before anyone else gets a chance.