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Whisk together the vinegar, rosemary, and salt and pepper, to taste. Slowly whisk in the olive oil.
Peel the eggplant and cut crosswise into 1/3-inch slices (12 slices total). Cut the tomatoes crosswise into 1/3-inch slices (8 slices total). Put the vegetables on a tray and brush generously with the dressing.
On the grill's hot side, grill the eggplant until just cooked through, 2 to 3 minutes per side, brushing with more of the dressing. Grill the tomato slices for 1 minute per side. (The vegetables should retain their shape.) Transfer the vegetables to a tray as they finish grilling.
Arrange 4 stacks of vegetables on the cooler side of the grill: start with the eggplant, add a slice of tomato, then add some crumbled cheese. Repeat. Cover the grill and cook the stacks or 3 to 5 more minutes or until the feta melts. Serve immediately.