Preheat your oven to 350°F. Line a rimmed baking sheet with unbleached parchment paper and set it aside.
In a small, heat-safe bowl, place the chopped butter and chopped chocolate. Place over a small saucepan of simmering water, making sure the water doesn’t touch the bowl. Cook, stirring occasionally, until the butter and chocolate are melted and smooth.
Remove from the heat and set aside to cool until no longer hot to the touch. Alternatively, melt the butter and chocolate in the microwave in 30-second bursts at 60% power.
In a large bowl, place the cake mix, and whisk to break up any lumps. Add the mascarpone or cream cheese, melted butter and chocolate, vanilla, and eggs, mixing well after each addition. The dough will be thick.
Drop the dough by rounded tablespoonfuls onto the prepared baking sheet, 1 inch apart. With wet hands, roll each piece of dough into a ball, and then flatten into a disk about 1/2-inch thick.
Bake the cookies in the center of the preheated oven for 8 to 10 minutes, or until puffed and beginning to take on a crackled appearance on top. Allow to cool for 10 minutes on the baking sheet before transferring to a wire rack to cool completely.