Preheat the oven to 350°F (180C). Spray or butter the bottom and sides of the cake pan, then line the bottom with a disc cut from parchment paper. Set aside.
In a large mixing bowl, whisk together the flour, baking powder, and kosher salt.
In a separate bowl, whisk the egg, egg yolks, and sugar until combined, and the mixture is pale (about 1 minute). Add in ½ of the mascarpone, the melted butter, vanilla, and lemon zest. Continue whisking until the mixture is consistent and smooth in texture.
Add the egg and butter mixture to the dry ingredients. Fold or gently whisk everything together just enough to coat the flour and create a smooth batter. Pour into the prepared cake pan, and spread into an even layer.
Use a small spoon to remove the prunes from the syrup one at a time, draining each of any excess syrup. Dot them throughout the batter to cover the cake evenly–it’s okay if some of these touch. Reserve the syrup for serving.
Bake the cake 45-60 minutes on a center rack, until the top is golden brown throughout and firm to the touch–a toothpick inserted into the center will come out wet but mostly clean. Use a large piece of foil to tent the cake if it’s getting too much color before cooking all the way through. Let the cake cool completely in the pan.