Instructions

Adjust oven rack to lower-middle position and heat oven to 350 degrees. Line 12-cup muffin tin with paper liners.
Working in batches, use food processor fitted with shredding disk to process beets until shredded. Transfer to bowl and microwave, covered, until beets are tender and have released their juices, about 4 minutes, stirring halfway through microwaving. Fit now-empty processor with chopping blade and transfer cooked beets to processor.
Microwave chocolate in separate bowl at 50 percent power, stirring occasionally, until melted, about 2 minutes. Whisk in cocoa and oil until smooth and transfer chocolate mixture to food processor with beets; let cool slightly.
Process beets and chocolate mixture until smooth, about 45 seconds, scraping down sides of bowl as needed. Add sugar, eggs, milk, vanilla, baking soda, and salt and process until sugar is mostly dissolved and mixture is emulsified, about 15 seconds. Add flour and pulse until just incorporated, about 5 pulses; do not overmix.
Divide batter evenly among muffin cups. Bake cupcakes until toothpick inserted in center comes out clean, 20 to 22 minutes, rotating tin halfway through baking. Let cupcakes cool in muffin tin on wire rack for 15 minutes. Remove cupcakes from muffin tin and let cool completely, about 1 hour.
Mound 1 tablespoon frosting in center of each cupcake. Using small icing spatula or butter knife, spread frosting to edge of cupcake, leaving slight mound in center. Top with sprinkles, if desired. Serve immediately.