Set the oven to 375 °F (190 °C) and brush a 9 × 13 in baking dish with a thin film of olive oil.
Combine mozzarella, cottage cheese, scallions, beaten eggs, Italian herb blend, and a judicious pinch of salt and pepper in a large mixing bowl; keep this cheese mixture nearby.
Warm olive oil in a deep skillet over medium-high heat, then sauté zucchini and mushrooms until they begin to release moisture and take on light color; season with salt and pepper during cooking.
Add the cubed, pre-salted chicken to the skillet and continue sautéing about 5 minutes, just until the exterior turns golden.
Tip the skillet contents into a colander, allowing excess liquid to drain thoroughly.
Fold the drained vegetables and chicken into the prepared cheese mixture until all components are evenly coated.
Spread the combined mixture into the oiled baking dish, level the surface, and sprinkle grated Parmesan over the top.
Bake 30–40 minutes, or until the casserole is deeply golden and the cheese bubbles at the edges.
Remove from the oven; let the dish stand 5–10 minutes to settle before slicing and serving.