Bring a large pot of salted water to a boil; first, cook pasta per package instructions until al dente.
Reserve 1/2 cup pasta water; then drain.
Meanwhile, heat olive oil and 2 tbsp butter in a large skillet over medium heat. Add garlic and cook about 30 seconds until fragrant.
Add carrots and broccoli; sauté 4–6 minutes until tender‑crisp.
Stir in peas and cook 1–2 minutes.
Add pasta, remaining butter, and reserved pasta water.
Toss to coat so the sauce becomes silky and clings to the noodles.
Stir in Parmesan if using.
Season with salt and black pepper, garnish with parsley, and serve immediately.