Preheat oven to 400°F (200°C).
- In a large oven-safe skillet or baking dish, toss carrot sticks with 2 tablespoons olive oil, garlic, oregano, red pepper flakes, salt, and pepper.
- Roast carrots for 15 minutes until slightly tender.
- Meanwhile, cook pasta in salted boiling water for 4-5 minutes less than package instructions; drain.
- Add cooked pasta to the skillet with carrots. Pour in vegetable broth and stir to combine.
- Sprinkle crumbled feta evenly over the top and drizzle with remaining olive oil.
- Bake uncovered for 20-25 minutes until pasta is tender and feta is golden and bubbly.
- Garnish with fresh parsley or basil before serving.