How to Make It
Make the dressing In a food processor, pulse the egg yolks, lemon juice, anchovies, chopped parsley, chives, mustard and vinegar until smooth. With the machine on, drizzle in both oils until smooth. Transfer to a bowl, cover with plastic and refrigerate. Clean out the processor.
Make the brussels sprouts Thinly slice 2 cups of the smallest brussels sprouts and transfer to a large bowl. In a food processor fitted with the slicing blade, shred the remaining brussels sprouts; transfer to the bowl. Toss with the olive oil, vinegar and garlic and season with salt and pepper. Cover and let stand for 1 hour. Toss in the Caesar dressing and cheese. Garnish with parsley and serve.