1. Preheat oven to 400°F and grease a large baking sheet with olive oil.
2. Trim the stems off the Brussels sprouts, leaving a bit to hold them together, and slice in half through the stem. Pile onto the baking sheet.
3. In a small bowl, whisk together the olive oil and 2 tablespoon of balsamic vinegar. Pour over the sprouts and massage with hands. Spread in a single layer and sprinkle with salt and pepper.
4. Bake for 20 minutes, remove and turn the sprouts over, then roast for another 20 minutes until fork-tender.
5. Transfer to a large mixing bowl, drizzle with the remaining tablespoon of balsamic vinegar, and toss. Add cranberries and feta, and toss again. Taste and adjust seasoning as needed.