Add the zucchini, sweet potatoes, and tomatoes to a baking sheet. Drizzle with olive oil, and season with garlic powder, smoked paprika, oregano, salt, and black pepper. Toss everything together until evenly coated.
Spread the vegetables into an even layer. Roast for 25–30 minutes, stirring halfway through, until the sweet potatoes are tender, and the vegetables are lightly caramelized.
To assemble the bowls: Divide the cooked barley evenly among 4 bowls (about ¾ cup per bowl). Top each bowl with a serving of roasted vegetables, feta cheese, and fresh chopped parsley.