Prepare the sauce by making 1 batch of my homemade marinara sauce. If you are using store-bought marinara or pasta sauce, skip to cooking the pasta. Cook the pasta by bringing a large pot of heavily salted water to a boil. Add 1 pound ziti pasta and cook according to the package instructions, pulling it about 2 minutes short of al dente so it can finish cooking in the oven.
Drain the pasta, rinse briefly with cold water, and set aside.
Sauté the vegetables by heating 2 tablespoons olive oil in a large skillet over medium heat. Add 2 diced red, yellow, or orange bell peppers, 1 diced medium zucchini, and 1 teaspoon kosher salt and cook, stirring occasionally, for 6 to 7 minutes, or until softened.
Stir in 3 minced garlic cloves, 1 teaspoon Italian seasoning, and ½ teaspoon black pepper into the vegetables and cook for 1 minute more, until fragrant. Remove from the heat and stir in 1/2 cup halved Kalamata olives.
Heat oven to 425°F and arrange a rack in the middle.
Make the ricotta mixture by stirring together 16 ounces whole milk ricotta, 1 large egg, 1/2 cup grated cheese, ½ cup chopped fresh basil, and 1/2 teaspoon kosher salt in a large bowl until well combined.
In a large bowl, or the pot used to cook the pasta, combine the cooked ziti with 1 cup heavy cream, and 2 1/2 cups tomato sauce. Stir until the pasta is evenly coated.
Layer the casserole by spooning the remaining tomato sauce into the bottom of a 4-quart (9 x 13-inch) baking dish. Add half of the pasta mixture and half of the sautéed vegetables.
Dollop with half of the ricotta mixture and scatter half of the 16 ounces of fresh mozzarella balls over the top. Repeat the layers once more. Sprinkle 1/4 cup grated cheese over the top.
Bake the ziti by placing the baking dish on a parchment-lined sheet pan to catch any drips. Bake for 30 to 40 minutes, or until the edges are bubbling and the cheese on top is melted and nicely browned.
Serve the baked ziti after letting it rest for 5 to 10 minutes so the layers can set. Scatter with additional fresh basil and grate more Parmesan over the top, if desired.