Preheat oven to 400°F. Toss Brussels sprouts and chickpeas with 2 tablespoons olive oil, salt, and pepper on a large baking sheet. Arrange Brussels sprouts cut-side down.
Roast for 20-25 minutes, stirring halfway through, until Brussels sprouts are golden brown and crispy on the edges and chickpeas are slightly crunchy.
While vegetables roast, whisk together balsamic vinegar, honey, Dijon mustard, remaining 1 tablespoon olive oil, salt, and pepper in a small bowl to make the dressing.
Remove roasted vegetables from oven and transfer to a large serving bowl. Add dried cranberries and chopped pecans, tossing to combine.
Drizzle the dressing over the salad and toss gently. Top with crumbled feta cheese and serve warm or at room temperature.