Prepare the vinaigrette by whisking together olive oil, white balsamic vinegar, Dijon mustard, granulated sugar, salt, and black pepper in a small bowl. Set aside.
In a dry skillet, toast the walnuts over low heat until they turn golden brown and emit a nutty aroma. Set aside to cool completely.
Rinse and drain the Brussels sprouts, leaving the stems intact but removing any bruised or damaged outer leaves. Dry them thoroughly by patting with a paper towel.
Using a mandoline or sharp knife, shave each Brussels sprout thinly by holding onto the stem end and slicing carefully. Discard the tough stem ends. You should have around 5–6 cups of shaved Brussels sprouts. Transfer to a large mixing bowl.
Once cooled, coarsely chop the walnuts and add them to the mixing bowl with the shaved Brussels sprouts, dried cranberries, and sliced red onion. Gently toss to combine.
Just before serving, whisk the vinaigrette again and pour it over the Brussels sprout mixture. Toss gently to coat all ingredients evenly with the dressing.
Arrange the salad on a serving platter and sprinkle with crumbled goat cheese. If using plain goat cheese, drizzle honey over the top for a touch of sweetness as desired.