Trim the zucchini, then cut it crosswise on the bias into 1⁄4-inch thick slices.
Heat 1 tablespoon of the oil in a large nonstick skillet.
Cook the zucchini in a single layer, in batches, turning once, until crisp tender with bright green edges, about 2 to 3 minutes.
Remove to a bowl, and cool 10 minutes.
To the bowl add the remaining oil, and the vinegar, salt, pepper, and oregano.
Mix gently to coat the zucchini.
On a serving plate, arrange the zucchini in an overlapping pattern.
Top with the crumbled cheese.
Serve at room temperature.