Heat 1 teaspoon oil in a large nonstick skillet over medium heat; add bread crumbs and cook, stirring often, until golden, about 3 minutes. Remove from heat; stir in Parmesan cheese. Spoon bread crumbs into a small bowl; set aside.
Heat remaining 1/4 teaspoon oil in same skillet. Add garlic, cook, stirring, until fragrant, about 30 seconds. Gradually add half of spinach to skillet, tossing mixture and adding more spinach as some of it cooks down. Continue cooking and tossing, until spinach is wilted and tender, about 2 to 3 minutes. Remove from skillet and repeat with remaining spinach.
Return cooked spinach to skillet; add salt and toss over low heat. Transfer to a serving bowl and sprinkle with crumbs. Or toss with half of crumbs and sprinkle remaining crumbs over each serving. Yields about 3/4 cup spinach and 2 tablespoons crumbs per serving.