Preheat oven to 400°F. Toss sprouts and chickpeas with 2 tablespoons oil, salt, and pepper on a large baking sheet; arrange sprouts cut-side down.
Roast 20-25 minutes, stirring halfway, until sprouts are golden brown with crispy edges and chickpeas slightly crunchy.
Meanwhile, whisk vinegar, honey, mustard, remaining 1 tablespoon oil, salt, and pepper in a small bowl.
Transfer roasted vegetables to a large serving bowl; toss with cranberries and pecans.
Drizzle with dressing; toss gently. Top with feta; serve warm or at room temperature.