Preheat the oven to 300°F (150°C) and place the oven rack at the lowest position.

Whisk egg yolks, ¼ cup white sugar, and vanilla together in a heatproof bowl until smooth. Gradually add hot cream whisking continuously to combine.

Set the bowl over a double boiler and cook gently, stirring until the mixture thickens.

Transfer the mixture into ramekins or a baking dish and bake in the oven until set but slightly jiggly, about 20–30 minutes.

Chill the baked crème brûlée in the refrigerator for 2 hours.

Combine 2 tablespoons white sugar and brown sugar. Sprinkle evenly over chilled crème brûlée.