Begin by preheating your oven to 325°F and preparing your baking vessel—either an 18-ounce shallow dish or 6–8 individual ramekins with a light coating of grease.
In a bowl, beat 4 extra-large egg yolks together with 3 tablespoons (30g) of granulated sugar and a few drops of vanilla extract until the mixture becomes pale and well combined.
In a separate saucepan, heat 1¼ cups (300ml) of half-and-half and 1¼ cups (300ml) of heavy cream together until the mixture reaches just below boiling point.
Allow the cream mixture to cool slightly before slowly whisking it into the egg yolk mixture, stirring constantly to prevent the eggs from scrambling and creating a smooth custard base.
Pour the custard into your prepared dish or ramekins, then carefully place them into a roasting pan that has been filled halfway with hot water—this water bath guarantees gentle, even cooking that prevents the delicate custard from curdling or developing an undesirable texture.
Bake for 45 minutes if using one shallow dish, or 25–30 minutes if using individual ramekins, until the custard is set but still slightly jiggly in the very center. Remove from the oven and allow to cool completely, then cover and refrigerate overnight, which allows the flavors to develop and the custard to firm up completely.
When ready to finish the dessert, preheat your broiler to high heat. Remove the chilled custard from the refrigerator and sprinkle about ¼ cup (55g) of demerara sugar evenly across the top of each ramekin or the shallow dish.
Place under the broiler for 3–4 minutes, watching closely to guarantee the sugar melts and caramelizes to a golden-brown color without burning. Remove from heat and allow to cool for a few minutes, then refrigerate for 2–3 hours before serving, which allows the caramelized topping to slightly soften while maintaining its satisfying crunch.