In a large nonstick skillet, heat oil over medium heat. Add potatoes, cut sides down, and garlic; cook, turning potatoes occasionally, until golden brown, 6 to 8 minutes.
Add rosemary and 1/2 cup water; reduce heat to medium-low. Cover; cook, turning potatoes occasionally, until tender and water has evaporated, 15 to 20 minutes (check after 15 minutes and add more water if potatoes are not done).
Strip leaves from rosemary sprigs; discard stems and scatter leaves. Season potatoes with salt and pepper. Serve immediately.