Preheat oven to 350 degrees F. Grease a 13 x 9 inch baking pan with nonstick cooking spray.
Place chocolate in a microwave-safe bowl. Transfer to microwave, and melt chocolate, stirring every 30 seconds, until melted, about 3 minutes. Set aside to cool.
Whisk to combine flour, baking soda, and salt in a medium bowl. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, combine sugar, eggs, and oil. Beat until well combined, about 2 minutes. Add beets, cooled melted chocolate, and vanilla. Beat until combined. Decrease speed to low and gradually add dry ingredients, scraping down the sides of the bowl as necessary.
Pour into prepared pan and smooth top. Transfer to oven and bake until a toothpick inserted into the center comes out clean, about 25-28 minutes. Cool completely on a rack.
Meanwhile, combine cream cheese and butter in the bowl of a stand mixer fitted with the paddle attachment. Beat on medium speed until fluffy and well combined. At low speed, gradually add confectioners’ sugar, beating until entirely smooth and well-incorporated. Add vanilla and a pinch of salt. Beat to combine.
With a spatula, top cake with frosting, swirling to create peaks and valleys. Cut into squares and serve.