Prepare the Brussels sprouts:
- 1
Preheat oven to 425°F. Trim the stem ends and remove any damaged outer leaves. Halve the sprouts lengthwise, quartering particularly large ones.
- 2
Toss with 2 tbsp olive oil, salt, pepper, and thyme. Spread on a large baking sheet, cut sides down.
Begin roasting:
- 3
Roast the Brussels sprouts for 12–15 minutes, until the cut surfaces begin to brown.
Prepare the apples:
- 4
While the sprouts roast, core the apples and cut into thick wedges, approximately 3/4 inch.
- 5
Leave the skins on for color and texture.
- 6
Toss with the remaining 1/2 tbsp olive oil and the optional smoked paprika.
Add the apples:
- 7
Remove the baking sheet and gently distribute the apple wedges between the Brussels sprouts.
- 8
Return to the oven for another 12–15 minutes, until the sprouts are deeply golden and the apples are tender but still hold their shape.
Toast the walnuts:
- 9
While everything finishes roasting, toast the walnuts in a dry skillet over medium-low heat for 3–5 minutes, stirring frequently.
- 10
Remove from heat once fragrant.
- 11
Prepare the finishing dressing:
- 12
In a small bowl, whisk together the apple cider vinegar and optional Dijon mustard.
- 13
If using butter, melt it and whisk it into the dressing.
Finish and serve:
- 14
Transfer the roasted sprouts and apples to a serving bowl.
- 15
Toss lightly with the dressing, sprinkle with the toasted walnuts, and adjust salt and pepper to taste.
- 16
Serve warm.
