Adjust oven rack to lower-middle position and heat oven to 350° F. Line a 12-cup muffin tin with paper or foil liners.
Working in batches, use a food processor fitted with a 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 a chopping blade and transfer beets to processor. Microwave chocolate in a second 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 over mix.
Divide batter evenly among prepared muffin cups. Bake until a toothpick inserted in center comes out clean, 20 to 22 minutes, rotating muffin 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 on rack, about 1 hour. Spread or pipe cream cheese frosting evenly on cupcakes and finish with beet sprinkles. Serve.
*cream cheese frosting recipe
