Blend all dressing ingredients until smooth. Taste and adjust seasonings if needed, then set aside.
Shave brussels sprouts using a food processor with grater attachment, pulsing until finely shredded.
Place shaved brussels sprouts in a large bowl and add sliced green onions and grated pecorino.
Toast walnuts in a dry skillet over medium heat until golden and fragrant, stirring frequently.
Add warm toasted walnuts to the salad bowl.
Pour dressing over salad ingredients and toss thoroughly to combine.
Serve immediately for best flavor and texture.