Step 1Heat the oven to 350 degrees.
Step 2Heat the oil in a large nonstick skillet over medium-high heat. Add the zucchini, oregano, salt and pepper to taste. Cook, stirring, until some of the zucchini just starts to wilt, about 2 to 3 minutes. Add the spinach. Toss into the zucchini. Cook, stirring, until some leaves begin to wilt. Remove from the heat.
Step 3Transfer to a shallow baking dish, spreading evenly. Sprinkle the cheese over the top. (This can be baked now or cooled and refrigerated overnight, well covered.)
Step 4Bake, tented with foil, until the liquid is bubbling, about 40 to 45 minutes. (Remove the foil after 35 minutes so the cheese browns a little.) Carefully drain off the accumulated juices. Serve hot.