Heat 2 tablespoons olive oil in a large skillet and cook zucchini slices in batches until soft and lightly browned on both sides, 5 to 10 minutes. Add more olive oil as needed. Remove zucchini slices from skillet and drain on paper towels.
Sprinkle zucchini slices with feta and roll up. Secure each roll with a tooth pick.
Set zucchini rolls into a dish that is as deep as the rolls are high, and sprinkle with garlic, Italian herbs, and balsamic vinegar. Cover and marinate in the refrigerator for 1 to 2 days.
