For the vinaigrette: In a medium bowl, combine the lemon juice, orange juice and shallots. Let stand 5 minutes so the acidity in the juice can begin to break down the shallots. Whisk in the Dijon and honey until well combined. Slowly whisk in the oil until emulsified. Season aggressively with salt and add pepper.
For the salad: Add the sprouts, apricots, hazelnuts and pecorino to the vinaigrette and toss to coat. The salad can be dressed 15 to 20 minutes in advance if you like more tender Brussels sprouts.