Prep the oven and pan: Preheat to 400°F (200°C). Lightly grease a large baking dish with 1 teaspoon olive oil.
Hollow the zucchini: Trim ends and slice each zucchini lengthwise.
Use a spoon to scoop out the centers, leaving a 1/4-inch border to form “boats.” Finely chop the scooped zucchini flesh and set aside.
Season the boats: Brush cut sides with 1 tablespoon olive oil. Sprinkle with salt and pepper. Place in the baking dish, cut side up.
Sauté aromatics: Heat the remaining olive oil in a skillet over medium.
Add onion and cook 3–4 minutes until translucent. Stir in garlic and the chopped zucchini flesh; cook 2–3 minutes until most moisture evaporates.
Make the filling: Reduce heat to low. Stir in shredded chicken, cream cheese, sour cream, Italian seasoning, smoked paprika, red pepper flakes, salt, and pepper.
Mix until creamy and warmed through. If using marinara, fold it in now. Stir in half the Parmesan and half the mozzarella.
Fill the boats: Spoon the chicken mixture into each zucchini, packing it evenly.
Top with remaining mozzarella and Parmesan.
Bake: Cover loosely with foil and bake 15 minutes. Remove foil and bake another 10–12 minutes until zucchini is tender and cheese is bubbly and golden at the edges.
Finish and serve: Rest 5 minutes. Sprinkle with fresh parsley or basil.
Taste and adjust seasoning if needed. Serve warm.