In a small bowl, toss the breadcrumbs, sage and 2 tbsp. EVOO. Transfer to a medium skillet and cook, stirring, over medium heat until golden and crisp, 6 to 8 minutes. Season with salt and pepper.
Wash the squash well, but don't peel. Slice off one end of each and, using a long spoon, scrape out the seeds. Cut crosswise into 1/2-inch-thick rounds.
In a large skillet, heat the remaining 1/4 cup EVOO over medium-high heat. Working in batches, add the squash rounds and cook, undisturbed, until golden and crisp around the edges, about 5 minutes. Flip and cook until tender when pierced with a fork, about 3 minutes more. Drain on a paper towel.
Transfer the squash rings to a platter and season with salt and pepper. Garnish with the breadcrumbs and parmesan.