Place vinegar in a small bowl; whisk in oil. Add rosemary, 1/2 teaspoon salt, and 1/4 teaspoon pepper. In a shallow nonreactive dish, arrange mushrooms, stem-side down, in an even layer. Brush each mushroom cap with marinade, and set aside. Cover with plastic wrap, and let stand at room temperature for 15 to 20 minutes.
Trim rosemary sprigs to a length to hold two mushroom caps, leaving about 1 inch of the skewer exposed. Thread rosemary, stem-end first, crosswise through the mushrooms, removing rosemary needles if needed to skewer. Heat a grill pan over medium-high heat until warm. Cook the skewered mushrooms, stem-side up, on the grill for about 6 minutes, until subtle grill marks appear. Serve warm with remaining vinaigrette on the side, if desired.