In a large bowl, whisk the whole eggs and egg yolks with ¾ cup / 150g (5.3 oz) of the sugar until the mixture is pale, thick, and creamy.
In a separate saucepan, combine the milk and heavy cream and gently heat over medium heat until it's hot and steaming, but not boiling.
Very slowly, pour the hot milk and cream mixture into the egg and sugar mixture in a thin, steady stream, whisking constantly to temper the eggs. This prevents them from scrambling.
Once combined, stir in the vanilla extract and set aside.
To make the caramel, add the remaining 1 cup / 200g (7.1 oz) of sugar to a heavy-bottomed saucepan over medium-low heat.
Let the sugar melt without stirring, gently swirling the pan occasionally.
Once it melts and turns into a beautiful light-brown, amber-colored syrup (about 5-8 minutes), immediately remove it from the heat.
Working quickly and carefully, divide the hot caramel among 6 or 8 individual custard cups or ramekins. Immediately tilt and swirl each cup to coat the bottom and a little way up the sides. The caramel will harden almost instantly.
Set the cups aside.
Preheat your oven to 350°F / 175°C.
Strain your custard mixture through a fine-mesh sieve directly into the prepared caramel-coated cups.
Place the cups in a large baking pan and carefully pour hot water into the pan until it comes halfway up the sides of the cups, creating a water bath (bain-marie).
Cover the tops of the custards loosely with a sheet of aluminum foil. This prevents the tops from browning and helps them cook gently.
Bake for 45 to 50 minutes.
The custards are ready when they are mostly set but still have a slight jiggle in the very center. A sharp knife inserted near the center should come out clean. Carefully remove the pan from the oven and let the custards cool in the water bath.
Once cool enough to handle, remove the cups from the water bath, let them cool completely to room temperature, then cover and chill in the refrigerator for at least 4 hours, or preferably overnight.
To serve, run a thin knife around the inside edge of each custard cup.
Place a rimmed serving plate over the top of the cup and, holding them together firmly, quickly invert. The custard will release onto the plate, with the caramel sauce pooling beautifully around it.
Serve chilled and enjoy!
When making the caramel, resist the urge to stir with a spoon at first. Gently swirl the pan to help the sugar melt evenly, which prevents crystallization and ensures a smooth syrup.
