Caramel espresso flan cake

Directions

1. NOTE: Unless you trust your cake-pan to be absolutely non-stick, I would strongly recommend to lightly oil the entire pan plus parchment-line the part where it’s in contact with the sponge cake batter (instruction below).
2. TO PRHEAT THE OVEN: Place a large baking-dish/sheet (large enough to hold the cake-pan) that’s at least 2?-deep inside the oven, and pour 1? of water inside. Turn the oven on 400ºF/200ºC and close the oven.
3. TO MAKE THE CARAMEL ESPRESSO FLAN: Lightly oil the interior of a 8? round cake-pan, set aside. Cook granulated sugar and water in a medium-size pot (this is the same pot we’re gonna use throughout the recipe) over medium heat, and bring it to a boil. Gently swirling the pot, and cook until the sugar turns light brown in color. At this point, turn off the heat and keep swirling. The sugar will continue to darken into a deep, amber-color (if not residual heat is left, return the pot to medium heat for a bit). Pour all the caramel into the cake-pan (a thin layer may be left inside the pot), and quickly swirl the pan to distribute an even layer of caramel on the bottom before it hardens (if it hardens too quickly, warm the bottom of the cake-pan over low heat). Set the cake-pan aside.
4. Dip the bottom of the pot in a bit of water to cool it down. Add the half-half and ground espresso beans, and return to medium heat. Stir gently with a wooden spoon and bring to a bare simmer, then turn off the heat completely (the leftover caramel should melt back into the cream). Let it brew for 5 min. Meanwhile, whisk 4 large yolks, 2 large eggs and sweetened condensed milk together in another bowl until smooth. Slowly pour the espresso cream, through a very fine sieve, into the egg-mixture. Whisk quickly to combine. Discard the ground espresso in the sieve, then pour the espresso/egg-custard into the cake-pan, through the same sieve again. Cut a thin strip of parchment paper, lightly oil one side and line the inside of the cake-pan just above the custard. Then set aside.
5. TO MAKE THE BUTTER-ROUX CAKE: Wash the same pot clean and towel dry (use another pot if you prefer). Add the unsalted butter and cook over medium-high heat. Once it’s melted and starts to bubble, add the all-purpose flour all at once. Whisk quickly until even then turn off the heat. Add the whole milk and light brown sugar and whisk until the sugar has melted. The cold milk and sugar should’ve cooled the roux enough so it doesn’t cook the egg yolk. Now add the egg yolks and vanilla extract, and whisk until thick and even. Beat the egg white with 1/2 tsp of cream of tartar with a stand-mixer or handheld-mixer, until soft peaks form.
6. Add 1/2 of the beaten egg whites into the roux/egg yolk-mixture, and stir gently until evenly combined. Then add the rest of the egg whites, and instead of stirring, gently fold it into the mixture with a spatula until even. Pour the cake batter into the cake-pan. Don’t freak out if it seems to sink to the bottom through the custard! It will float back up because the batter is lighter than the custard! Smooth the top, and we’re ready to bake.
7. TO BAKE THE CAKE: Carefully place the cake-pan in the middle of the deep baking-sheet with water (which is hot by now). Lower the temperature down to 340ºF/170ºC, and bake for 50 ~ 55 min. A wooden skewer should come out completely clean from the center of the cake. Let the cake cool for 30 min on a cooling rack. Then gently pull away the parchment paper, and score the bottom-edge of the cake with a small knife. Place a large plate, up-side down over the cake-pan, then quickly invert it. Remove the cake-pan, and the cake should come out effortlessly. If there’s a layer of caramel on the bottom of the pan that’s too thick to pour out, add 1 tsp of water and warm over low heat until the caramel’s loose again. Pour over the cake. The cake gets better with time as the sponge cake absorbs the caramel and…. urgh! I can’t even…