Prepare a 9-inch springform pan by cutting a round of parchment paper to fit the bottom. Butter the sides. Set aside.
Melt butter over medium heat in a small, heavy-bottomed saucepan. Cook until the butter foams and the milk solids turn golden brown. Stir occasionally whilst browning the butter and do not leave unattended. This takes about 5 minutes. Immediately transfer to a 3-quart, heatproof mixing bowl to cool slightly. Add the heavy cream and cool completely but still in a liquid state.
Meanwhile whisk together the flour, salt, espresso powder, baking powder, and baking soda in a small bowl and set aside.
When the butter mixture is cooled, add the granulated sugar and beat with the butter-cream mixture with a handheld mixer, or in a stand mixer, on medium-high speed. When the granulated sugar is incorporated, add the brown sugar and continue beating on medium-high speed until the mixture is light, fluffy. Stop to scrape the sides of the bowl as needed.
Add egg and egg yolk one at a time, beating until well combined after each addition. Beat in vanilla extract. The mixture should have at least doubled in volume from the beginning.
Add the flour mixture to the butter mixture, beating on low speed until just combined. Finish stirring by hand using a spatula as needed to incorporate the flour well, but don’t over mix. Fold in the chocolate chips to disperse evenly.
Transfer the dough into the prepared baking pan and gently pat into an even layer. Cover well with cling wrap and refrigerate overnight or up to 3 days.
When ready to bake, position an oven rack to the middle oven position. Preheat to 350° F.
Bake until the edges of the cake are golden brown and tolooks dry, about 40 – 45 minutes. Do not over bake.
Remove from the oven and let cool for 10 minutes, at which time remove the sides from the springform pan. Cool completely before garnishing and serving.
Garnish: This is optional as the cookie cake looks appealing as is. But to fancy it up, melt about 1/ 4 cup of chocolate chips in a small, heatproof ramekin (a few short bursts in the microwave works here). Use a small spoon, knife tip or wooden skewer to dip into the melted chocolate and spread onto the cookie cake as desired. Or just add fresh fruit, softly whipped cream, or (our favorite) ice cream.