Preheat oven to 400F degrees and place a rack in the middle. Rub a 9x9 gratin pan (or equivalent baking dish) with a bit of olive oil, sprinkle with lemon zest, and set aside.
Place the zucchini slices into a colander placed over a sink, toss with the sea salt and set aside for 10-15 minutes (to drain a bit) and go on to prepare the oregano sauce and bread crumbs.
Make the sauce by pureeing the oregano, parsley, garlic, 1/4 teaspoon salt, red pepper flakes, and olive oil in a food processor or using a hand blender. Set aside.
Make the breadcrumbs by melting the butter in a small saucepan over medium heat. Cook for a few minutes until the butter is wonderfully fragrant, and has turned brown. Wait two minutes, then stir the breadcrumbs into the browned butter.
Transfer the squash to a large mixing bowl. Add the potatoes and two-thirds of the oregano sauce. Toss until everything is well coated. Add the cheese and half of the bread crumbs and toss again. Taste one of the zucchini pieces and add more seasoning (salt or red pepper) if needed.
Transfer the squash to the lemon-zested pan, top with the remaining crumbs, and bake for somewhere between 40 and 50 minutes - it will really depend on how thinly you sliced the squash and potatoes - and how much moisture was still in them. You don't want the zucchini to go to mush, but you need to be sure the potatoes are fully baked. If the breadcrumbs start to get a little dark, take a fork and rake them just a bit, that will uncover some of the blonder bits. Remove from oven, and drizzle with the remaining oregano sauce.