Preheat oven to 350°F.
Prepare a 13x9-inch pan by lining the sides with strips of parchment paper and greasing the strips lightly with butter.
In a stand mixer with the whisk attachment, whip egg whites with ½ cup sugar, kosher salt, and cream of tartar on medium speed until frothy, then gradually increase to medium-high speed until stiff peaks form.
In a separate bowl, beat egg yolks with the remaining ½ cup sugar on high speed until pale, light, and moussey, forming a ribbon.
Slowly stream in the melted and cooled butter into the yolk mixture, followed by 2 teaspoons of vanilla extract.
Sift the all-purpose flour over the yolk mixture and incorporate on low speed.
Gently fold about a quarter of the whipped egg whites into the yolk mixture to lighten it.
Scrape the lightened yolk mixture into the remaining egg whites and fold until just combined, being careful not to overmix.
Pour the batter into the prepared pan and smooth into a single layer.
Tap the pan sharply on the counter to pop any large air bubbles.
Bake for 25-30 minutes, or until domed and golden brown.
While the cake bakes, prepare the milk soak by combining 1 cup heavy cream, 3 cups whole milk, 1 can sweetened condensed milk, ½ cup Cometeer or espresso, and a pinch of salt in a bowl. Whisk until the sweetened condensed milk is dissolved.
Once the cake is baked, invert it onto a cooling rack to cool completely.
After cooling, peel off the parchment strips and the film from the bottom of the cake.
Clean the 13x9-inch pan, line it with plastic wrap, and place the cake back into the pan.
Poke holes all over the cake using a fork or skewer.
Pour the milk soak evenly over the cake, ensuring it is fully saturated. The cake will absorb the liquid.
Cover the pan with plastic wrap and refrigerate for at least 24 hours to allow the cake to soak.
To prepare the topping, whip 8 ounces of chilled mascarpone cheese with 1 cup of chilled heavy cream and 2 teaspoons of vanilla extract until softly whipped.
Unmold the soaked cake onto a serving platter, pouring off any excess liquid.
Spread the whipped mascarpone mixture evenly over the top of the cake.
Grate 3 ounces of dark chocolate over the mascarpone topping.
