Cut the solid cylindrical top off the squash and remove the peel. (Set the bulbous base aside for another recipe.) Slice into very thin discs using a mandolin. Soak chips in a large bowl of ice water for 10-15 minutes. Pat dry with paper towels.
Heat peanut or vegetable oil 2-3" deep in a pot; bring temp up to 325°F Add sage and rosemary and fry until they stop sizzling and are crispy. Remove herbs and drain on paper towels. Crumble herbs and set aside.
Add squash chips to oil in small batches, frying each batch 2-3 minutes until crispy. Drain on paper towels, sprinkling with crumbled fried herbs, salt and parmesan cheese while still hot.