Preheat the oven to 425°F (220°C). Lightly brush or spray zucchini slices with olive oil and arrange in a single layer on a lightly greased baking sheet.
Roast the zucchini for 12–14 minutes until slightly softened, then transfer to paper towels to drain and cool.
Meanwhile, heat 2 tablespoons olive oil in a large skillet over medium-high heat. Add diced onion and minced garlic and cook 1 minute, stirring.
Push onion and garlic to the side and add the ground beef. Brown the beef, breaking it up with a spoon, until no longer pink, then drain excess grease.
Add tomato paste and crushed tomatoes to the skillet, season with 1/2 teaspoon salt, 1/4 teaspoon black pepper, and simmer on low for about 30 minutes.
Stir in the fresh spinach and cook just until wilted, then remove the meat sauce from the heat and set aside.
In a large bowl, combine ricotta, 1/2 cup grated Parmesan, 8 oz shredded mozzarella, 8 oz shredded Pepper Jack, 1 large egg, 1 tablespoon dried basil, 1 teaspoon Italian seasoning, 1/4 teaspoon red pepper flakes, and salt and pepper to taste; mix until well combined.
Lightly grease a 9×13-inch baking dish. Spread about 1/2 cup of the cheese mixture on the bottom of the dish.
Arrange one layer of roasted zucchini to cover the bottom, then spread half of the remaining cheese mixture over the zucchini and top with half of the meat sauce.
Add another zucchini layer, spread the remaining cheese mixture, then top with the remaining meat sauce. Finish with a final zucchini layer.
Top the lasagna with 1 cup marinara sauce and 1 cup shredded mozzarella for the final topping.
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 an additional 20–30 minutes until bubbly and golden; broil briefly if you want more browning.
Remove from oven and let the lasagna rest for 10–15 minutes before slicing and serving.
