Place a rack in the center of the oven, and preheat the oven to 350℉. Grease a 10 to 12-cup bundt pan with 2 tablespoons of butter, making sure to cover all of the crevices. Pour caramel sauce into the bottom of the pan; set aside.
In a large bowl, use an electric mixer on medium-speed to combine the brown sugar and ½ cup butter until light and fluffy, 3 to 5 minutes. Beat in the egg until combined.
In a medium bowl, whisk together the flour, cocoa powder, baking powder, baking soda and salt. Add half of the dry ingredients to the egg mixture and beat on medium-low speed until just combined. Add the coffee and beat until incorporated. Add the buttermilk and the remaining dry ingredients and beat just until combined. Pour the batter into the pan over the caramel.
MAKE THE FLAN:
Fill a large pot with water, and bring it to a boil over high heat.
In a large bowl, whisk together the eggs, condensed milk and vanilla until combined. Whisk in the half and half. Then pour the flan mixture slowly and carefully into the bundt pan.
Tightly cover the pan with foil and place the chocoflan in a large roasting pan or large pan of some sort. Transfer the pans to the oven, Pour boiling water into the larger pan until it reaches about halfway up the sides of the bundt pan.
BAKE:
Bake until a tester inserted into the center comes out mostly clean, 60 to 70 minutes. Move the bundt pan to a wire rack, and remove the foil. Let cool for 1 hour at room temperature, then refrigerate for at least 2 hours (or up to 2 days) before serving.
SERVE:
Loosen the cake by placing the bundt pan in a large bowl of hot water. Place a platter upside down on the bundt pan, then invert to unmold the cake. Spoon remaining caramel sauce from the pan over the top.