Heat oven to 350°F. Line a standard-size muffin tin with 12 paper baking cups.

In a food processor, process drained beets to a smooth puree. Set aside.

In a medium bowl, whisk flour, Dutch-process cocoa powder, baking soda, baking powder and salt until well combined. In a separate large bowl, whisk reserved beet puree, granulated sugar, buttermilk, melted butter, melted bittersweet chocolate and eggs until well combined. Using a spatula, fold dry ingredients into wet ingredients until just combined.

Divide batter evenly among lined muffin cups. Bake 25-27 minutes until a toothpick inserted in the center of each cupcake comes out clean. Transfer cupcakes to a cooling rack to cool completely.

Meanwhile, make the frosting: In a small microwave-safe bowl or cup, microwave milk on high 5 seconds until warm. Stir in instant espresso powder to dissolve. In a separate medium bowl, whisk powdered sugar and unsweetened cocoa powder until well combined.

In a large bowl with an electric hand mixer or in the bowl of a stand mixer with the whisk attachment, beat softened butter on high speed until light and smooth. Alternately stir in powdered sugar mixture and milk mixture, beginning and ending with powdered sugar mixture; beat well after each addition. Beat in vanilla. Beat on high speed 1 minute until frosting is smooth and airy.

Pipe frosting onto fully cooled cupcakes. Top with chocolate sprinkles, if desired. Store in an airtight container at room temperature for up to 3 days.