Preheat oven to 350°F. Spread walnuts on a baking sheet and toast until fragrant and golden, about 6 minutes. Transfer to a shallow dish and let cool.
Divide goat cheese into eight portions and roll into balls. Coat balls with toasted walnuts, pressing gently so that the nuts adhere.
Make the dressing: Combine Greek yogurt, olive oil, apple cider vinegar, Dijon mustard, honey and salt in a small bowl and whisk until smooth.
Combine Brussels sprouts and apple slices in a large bowl. Add dressing and toss. To serve, top salads with two goat cheese balls per serving.