To make this salad, start by preparing the dressing. Add all of the dressing ingredients (the olive oil, champagne vinegar, dijon mustard, honey, garlic, sea salt, and ground black pepper) to a blender and blend until smooth. Taste and adjust the seasonings as needed, then set it aside.
Next, prepare the salad. Wash and shave the brussels sprouts (if not shaved already) and add them to a large bowl. To shave them, simply add the brussels sprouts to a food processor with the grater attachment and lightly pulse them until they're finely shredded. You can also opt to use a mandolin, if you prefer.
Add the shaved brussels sprouts to a large bowl. Then, slice the green onions and grate the pecorino romano and add them to the bowl as well.
Prepare the walnuts by chopping them finely and adding them to a saucepan, on the stove, over medium heat.
Stir the walnuts to toast them until they're golden and fragrant, watching them carefully to ensure that they don't burn.
Once the walnuts are done, remove them from the heat and add them to the salad bowl.
Finally, pour the dressing on top of the salad and toss to fully combine. Once it's done, serve immediately and enjoy!