2 large eggs, at room temperature
For the frosting:
8 ounces semisweet chocolate, chopped, melted
1 tablespoon sugar
Pinch kosher salt
1/2 cup sour cream
Preheat oven to 350°F and line a standard 12-cup muffin tin with paper liners.
In a medium bowl, whisk together the flour, cocoa powder, baking soda, baking powder, and salt. In a large bowl, whisk together the sugar, beet purée, buttermilk, butter, chocolate, and eggs. Fold the dry ingredients into the wet.
Divide the batter evenly between prepared cups. Bake until the tops are puffed and a toothpick inserted into the center comes out with moist crumbs, 22 to 25 minutes. Transfer cupcakes to a rack to cool completely. Frost as desired.
To make the frosting: In a large bowl, whisk together the melted chocolate and the sugar and salt until smooth. Stir in the sour cream. Use immediately.