Slice the zucchini and squash into 1/4-inch thick rounds. In a large bowl, mix them with the olive oil, garlic powder, onion powder, oregano, and kosher salt.
Line two baking sheets with parchment paper. Place the vegetables in a single layer on the baking sheets. Roast for 8 minutes.
Remove the baking sheets from the oven and sprinkle evenly with the shredded Parmesan cheese. Return the sheets to the oven (on the opposite oven racks) and bake another 7 minutes until tender and the cheese is melted. Serve immediately.