Preheat the oven to 350 degrees F (175 degrees C).

Bring a large pot of lightly salted water to a boil. Cook lasagna noodles in boiling water, stirring occasionally, until tender yet firm to the bite, about 8 minutes. Drain; lay noodles flat onto a flat surface.

Heat olive oil in a small skillet over medium heat. Add garlic; cook and stir until fragrant, about 2 minutes. Transfer garlic to a large bowl. Add spinach, ricotta cheese, mozzarella cheese, and salt to the bowl; stir until evenly combined.

Spread a heaping ¼ cup spinach mixture into middle of each lasagna noodle. Roll noodles firmly around filling; arrange in a baking dish. Pour spaghetti sauce over rolls. Cover dish with aluminum foil.

Bake in the preheated oven for 30 minutes. Remove foil; continue baking 5 minutes more. Sprinkle Parmesan cheese over rolls to serve.