Preheat oven to 425 degrees F. Line a baking sheet with parchment paper.
Add all of the vegetables to a large bowl.
Drizzle with olive oil and sprinkle with garlic powder, oregano, basil, salt, and pepper. Toss to coat.
Spread vegetables in a single layer on the prepared baking sheet.
Roast for 20–25 minutes, stirring halfway, until vegetables are tender and lightly caramelized.
Remove from the oven and immediately sprinkle with feta cheese. Serve warm.