Mexican Coffee Flan

Preheat the oven to 200°.
Warm a 9-inch round × 2-inch deep cake pan in the oven.
In a heavy medium saucepan, cook sugar over medium heat, stirring frequently, until melted and golden brown, 5 to 8 minutes.
Quickly pour caramelized sugar syrup into the warm cake pan.
Using potholders to protect hands, tip the pan around to coat the bottom and about 1 inch up sides with the caramel syrup.
Set aside.
Raise the oven to 325°.
In a saucepan, bring about 2 cups of water to a boil.
Meanwhile, place in a blender jar the three milks, the eggs, egg yolk, vanilla, coffee, and brandy.
Mix on low speed 1 minute until completely mixed and smooth.
(If there is too much liquid, blend in 2 batches to prevent overflowing.
)
Pour the custard into the caramel-lined pan, set the pan into a larger pan, and place them on the middle rack of the oven.
Carefully pour boiling water into the larger holding pan to a depth of 1 inch.
Bake uncovered, 30 to 35 minutes, or until custard is set and a thin knife blade inserted in the center comes out clean.
Cool completely on a rack, then refrigerate, covered with plastic, about 8 hours or overnight.
To serve, run a thin knife around edge of pan between custard and pan.
(Press the knife against the pan, not the custard.
) Place a deep serving plate with a rim over the pan and invert to unmold the flan.
Carefully lift up pan and allow syrup to run over the flan.
Cut into wedges to serve.