Wash and cut all vegetables into evenly sized pieces so they cook uniformly. Try to keep sizes consistent so nothing overcooks or stays underdone. Mixing different vegetables also creates appealing color and texture.
Place vegetables in a large bowl and drizzle with oil. Sprinkle Greek seasoning, oregano, and smoked paprika over them, then toss thoroughly until every piece is coated. Proper seasoning ensures balanced flavor in every bite.
Spread vegetables in a single layer on a sprayed sheet pan so they roast instead of steam. Roast at 425°F (218°C) for 20–25 minutes, stirring halfway through. For crispier edges, broil for a few minutes at the end while watching carefully.
Once tender and slightly caramelized, remove the pan from the oven. Sprinkle feta cheese over the warm vegetables if desired. Taste and adjust seasoning before serving immediately for best flavor.