Place a rack in center of oven. Preheat oven to 400°F. Line a shallow baking pan with aluminum foil.
Cut green beans in half. Spread on prepared pan along with carrots, onions, peppers and thyme sprigs. Sprinkle with salt and pepper. Whisk garlic, olive oil, basil, paprika, salt and pepper together in a small bowl. Pour mixture over vegetables and toss to coat evenly. Roast for 20 minutes. Using a wide spatula, turn vegetables. Roast until tender, 15 to 25 minutes more.