Pat the quail dry with paper towels and arrange them skin-side down.
In a small bowl, combine the olive oil, minced garlic, dried rosemary or thyme, black pepper, and salt.
Rub the marinade over both sides of the quail. Cover and marinate for at least 30 minutes.
If the prunes are very dry, soak them in warm water for 10 minutes. Drain and pat them completely dry.
Place three prunes and a small sprig of fresh thyme in the center of each quail.
Fold the sides of each bird toward the center to enclose the filling and form a compact bundle.
Wrap each quail with three or four thin-cut bacon slices. Secure the loose ends with wooden toothpicks if necessary.
Preheat the oven to 375°F. Line a baking dish or rimmed baking sheet with parchment paper.
Arrange the quail in the prepared baking dish, leaving a little space between each bird.
Bake for 30–35 minutes, or until the bacon is golden and the thickest part of the meat reaches 165°F.
If the quail is cooked but the bacon needs more color, increase the oven temperature to 425°F or broil for 2–4 minutes.
Let the quail rest for 5 minutes. Remove all toothpicks before serving.