Place bread pieces in food processor and process until fine crumbs form.
Heat 1 teaspoon of olive oil in a large skillet over medium-high heat, swirling to coat. Add breadcrumbs, Italian seasoning, and a pinch of salt; cook until browned, about 2 minutes. Transfer breadcrumbs to bowl and carefully wipe out skillet.
Heat remaining olive oil in skillet over medium heat. Add onion and cook 3 minutes, stirring occasionally, until softened. Add zucchini and cook 10–12 minutes more, continuing to stir occasionally, until vegetables are golden brown in color and zucchini has softened. Add salt and pepper to taste and top with breadcrumb mixture and Parmesan cheese before serving.
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