1. Zest entire orange and juice half of it (about 1/4 cup).
2. In a 12-inch sauté pan, heat 1 tablespoon oil over medium-high heat. Sauté shallot for 1 minute. Add half of Brussels sprouts, cut-side down, in a single layer; sprinkle with 1/8 teaspoon salt. Cook for 4 minutes. Add half of orange juice, flip sprouts and cook for 4 minutes. Transfer sprouts to a large serving bowl. Repeat with remaining oil, sprouts, salt and juice. Add second batch of sprouts to serving bowl with first batch.
3. Toss sprouts with walnuts and orange zest and season with pepper. Serve warm, at room temperature or chilled as a salad.