Put ¼ cup of white sugar in a saucepan on medium heat. Do not stir; instead, shake the pan as the sugar melts. When it turns a deep copper color, pour it onto parchment paper and spread it out thinly. Let it harden completely, then break it into small, crunchy pieces.
In a saucepan, melt ¼ cup of sugar over medium heat. Shake the pan until the sugar becomes liquid and turns amber. Add 1 tablespoon of butter and stir until it melts. Gradually pour in ¼ cup of heavy cream while stirring. Let the mixture bubble for 1 minute, then remove it from the heat. Stir in a small pinch of salt. It will thicken as it cools.
Make two shots of espresso or brew ½ cup of strong coffee. Pour the hot espresso into your mug over the vanilla syrup. Heat the milk in a saucepan or frother until it steams, then froth it to create smooth foam.
Coat the inside of your mug with caramel brûlée sauce. Then, add vanilla syrup and hot espresso. Pour steamed milk down the side of the mug. Spoon foam on top and add a swirl of whipped cream. Finally, sprinkle a generous amount of crunchy caramel topping.