Preheat oven to 375 degrees. Brush a 9-by-5-inch loaf pan (6-cup capacity) with oil; dust with flour, and tap out excess.
In a small bowl, whisk oil, milk, and eggs. In a large bowl, whisk flour, Parmesan, baking powder, 1 1/2 teaspoons salt, and 1/4 teaspoon pepper; mix in zucchini, then egg mixture until just moistened (batter will be very thick, like biscuit dough).
Transfer batter to prepared pan; press in gently. Bake until a toothpick inserted in center comes out clean, 60 to 70 minutes (tent with foil if loaf starts to brown too quickly). Cool 15 minutes in pan; turn out loaf onto a rack to cool completely.
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