Preheat the oven to 350 degrees.
In a small skillet render the bacon. When almost crisp, add the olive oil and heat up. When the olive oil is hot, add the shallots and cook for a few minutes or until tender. Add the oregano and prosciutto and simmer for a minute. Remove the skillet from the heat and season to taste with salt and pepper.
Cut the baby zucchini in half. If you are using small zucchini, then cut them in half horizontally, then each half in quarters lengthwise. Set them in a lightly oiled gratin dish, skin side down. Sprinkle with the bacon mixture and scatter parsley on top. Cover and bake or 20 minutes.