Position an oven rack in center of oven and preheat oven to 325 degrees F.
a medium bowl, whisk together egg yolks and sugar.
In a medium-size saucepan, stir together the heavy cream and coffee. Set over
medium heat and bring to a boil, stirring to dissolve the coffee granules. Slowly
whisk the hot cream into the yolks. Whisk in the Kahlua and vanilla extract.
Ladle the mixture into 8 round shallow broiler-proof serving dishes about 3 inches wide
and about 1 inch deep. Set dishes in a shallow baking pan. Add boiling water to
the pan to come halfway up the sides of the dishes.
Bake until the tops are set,
about 30 minutes. The custards will remain jiggly until they are completely chilled.
Remove from the water bath and cool to room temperature.
Cover and chill overnight.
Heat broiler. With your fingers, press the brown sugar through a strainer onto
the custards in an even, fluffy layer. Wipe any excess sugar from the edges of the
Broil 5 to 6 inches from the heat source until the sugar liquefies and begins
to caramelize, rotating dishes to brown evenly and watching carefully to avoid burning.
Refrigerate the finished Creme Brulee for at least for hour before serving.