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1 cup shredded peeled zucchini
1 teaspoon salt, divided
3-1/2 cups all-purpose flour, divided
1 package (1/4 ounce) quick-rise yeast
5 tablespoons grated Parmesan cheese, divided
1 teaspoon sugar
1 cup warm water (120° to 130°)
1/4 cup butter, softened
Place zucchini in a small bowl; sprinkle with 1/2 teaspoon salt. Let stand for 5 minutes; drain.
Meanwhile, in another bowl, combine 3 cups flour, yeast, 2 tablespoons cheese, sugar and remaining salt. Add zucchini; toss to combine. Combine water and butter; add to dry ingredients. Stir in remaining flour to form a soft dough.
Turn onto a floured surface; knead until smooth and elastic, 6-8 minutes. Place in a greased bowl, turning once to grease top. Cover and let rise in a warm place until doubled, about 1 hour.
Divide dough in half; shape each portion into 12 balls. Place in a greased 13x9-in. baking pan. Sprinkle with remaining cheese. Repeat. Cover and let rise in a warm place until doubled, about 45 minutes.
Bake at 375° until golden brown, 20-25 minutes. Remove rolls from pan to a wire rack.