If time allows, pre-cook the zucchini to reduce moisture; otherwise proceed to the next step.
Preheat the oven to 425°F (218°C). Brush zucchini slices with olive oil and arrange in a single layer on a lightly greased baking sheet or use a grill pan.
Bake or grill the zucchini for 12–14 minutes until slightly softened, then transfer to paper towels to drain and cool.
Preheat a large skillet over medium-high heat and add 2 tablespoons olive oil.
Add the diced onion and minced garlic to the hot oil and cook, stirring, for about 1 minute.
Push the onion and garlic to one side, add the ground beef, brown and break it up with a wooden spoon, then cook until no longer pink; drain excess fat.
Stir in the tomato paste and crushed tomatoes, then add 1/2 teaspoon salt, 1/4 teaspoon black pepper, and Italian seasoning; reduce heat and simmer on low for about 30 minutes.
Add the fresh spinach to the meat sauce, stir until wilted, then remove from heat and set the meat sauce aside.
In a large bowl, combine ricotta, 1/2 cup grated Parmesan, 8 oz shredded mozzarella, 8 oz shredded Pepper Jack, the large egg, dried basil, Italian seasoning, red pepper flakes, and salt and pepper to taste; mix until well combined.
Lightly grease a 9×13-inch casserole dish with olive oil and spread about 1/2 cup of the cheese mixture on the bottom.
Arrange one layer of zucchini slices to cover the bottom, spread half of the remaining cheese mixture over the zucchini, then top with half of the meat sauce.
Add another layer of zucchini, spread the remaining cheese mixture, then top with the remaining meat sauce.
Finish with a final layer of zucchini, spread 1 cup marinara sauce over the top, and sprinkle 1 cup shredded mozzarella evenly over the sauce.
Preheat the oven to 375°F (190°C). Cover the dish with foil (not touching the cheese) and bake for 30 minutes.
Remove the foil and bake uncovered for another 20–30 minutes until bubbly; broil briefly if desired to brown the cheese.
Remove from the oven and let rest for 10–15 minutes before slicing and serving.
Garnish with parsley if desired and serve.