Prepare the zucchini: Place the sliced zucchini in a large colander and season lightly with salt. Set aside for about 1 hour to allow the zucchini to release its excess moisture. Drain well and pat the slices dry with clean kitchen towels or paper towels. This step helps prevent the Boureki from becoming watery.

Preheat the oven to 350°F (180°C).

Season the vegetables: Transfer the drained zucchini to a bowl or work surface. Drizzle with some of the olive oil and season with black pepper and oregano. Taste before adding additional salt since the zucchini has already been salted. Place the potatoes in a separate large bowl and toss with about ¼ cup olive oil, salt, and black pepper.

Prepare the cheese mixture: Combine the ricotta and crumbled feta in a bowl and mix until evenly combined.

Prepare the herbs: In another bowl, combine the finely chopped onion, mint, and parsley.

Prepare the baking dish: Drizzle 2-3 tablespoons of olive oil over the bottom of a 10 x 10-inch baking dish.

Build the first zucchini layer: Arrange half of the zucchini slices in an even layer over the bottom of the dish. Scatter half of the onion and herb mixture over the zucchini. Dollop one-quarter of the feta-ricotta mixture over the herbs, then lightly dust the layer with flour.

Add the first potato layer: Arrange half of the potatoes over the zucchini. Drizzle with half of the heavy cream and sprinkle with one-third of the shredded kefalotyri or Parmesan. Dollop another quarter of the feta-ricotta mixture over the potatoes.

Repeat the layers: Add the remaining zucchini, followed by the remaining onion and herb mixture, another quarter of the feta-ricotta mixture, and another light dusting of flour. Arrange the remaining potatoes over the top. Pour over the remaining heavy cream and add the remaining feta-ricotta mixture.

Finish the Boureki: Sprinkle the remaining kefalotyri or Parmesan evenly over the top. Finish with a little oregano and a drizzle of olive oil.

Begin baking uncovered: Place the Boureki on the center rack and bake, uncovered, for 25 minutes.

Cover and slow-bake: Remove the baking dish from the oven. Cover first with parchment paper and then tightly with aluminum foil. Return to the oven and bake for about 1½ hours, or until the vegetables are becoming very tender.

Brown the top: Remove the foil and parchment and bake uncovered for another 20-30 minutes, or until the potatoes are completely fork-tender and the top is beautifully golden.

Rest before serving: Allow the Boureki to rest for at least 20-30 minutes before slicing and serving. This gives the layers time to settle and makes it much easier to serve.