Preheat the oven to 350°F. Line a baking sheet with parchment paper for easy clean-up. Bake the walnuts for 5-8 minutes, until toasted and fragrant. Keep a close eye on them; they burn quickly.
In a large bowl combine kale leaves, 1 tablespoon olive oil, 1 tablespoon lemon juice and 1/4 teaspoon salt. Vigorously massage kale for 5 mins. After 5 mins the kale will have softened, decreased in size and will taste less bitter.
Add the brussels sprouts into the large bowl with kale.
Make the dressing by combining all of the remaining ingredients in a small bowl. Pour over the vegetables. Add the walnuts and toss well. Let the salad sit at room temperature for at least 30 minutes (or up to a few hours in the fridge) to allow the flavors to meld. Taste and adjust seasoning if necessary. Serve at room temperature.
Optional: top with 1 cup coarsely grated Parmigiano Reggiano.