Butter 9-inch cake pan, then line the bottom of the cake pan with parchment paper.
Place chocolate chips and butter into a stainless steel mixing bowl. Gently melt over double boiler. Stir well.
Place espresso and brown sugar in a sauce pot. Bring to simmer, stir to dissolve sugar.
Pour the hot sugar mixture over the chocolate; whisk until smooth and slightly cool.
Stir beaten eggs into chocolate mixture until blended. (Do not whip.)
Pour batter into the prepared cake pan. Place the cake pan in roasting pan. Pour enough hot water into the roasting pan to come halfway up sides of the cake pan.
Bake for approximately 45 minutes. Center of cake should be set.
Remove the cake pan from water and chill cake overnight.
Cut around the pan sides to loosen cake. Using oven mitts as an aid to hold the pan over a stove top burner, begin heating the bottom of the cake pan over low heat for 10 seconds to help release cake.
Place the serving platter on top of the pan. Hold pan and platter together tightly and invert.
Tap the pan to help release the cake. Lift the cake pan. Cake should come out of pan and onto platter. Peel off parchment.