Heat butter and oil in large stockpot to medium. Add carrot and onion, sprinkle with salt and pepper. Cook 2 minutes, then add green beans and other veggies (except peas).
Sprinkle with salt, pepper and add garlic powder. Cook, stirring occasionally, for 5-7minutes, or until veggies start to soften and onion is translucent.
Add tomatoes, stock and water, plus seasonings. Stir in beans and bring up to a simmer. Cook, covered, for 30-40 minutes until veggies are tender.
Mix in pasta during last 10 minutes of cooking.
Stir in peas, if using and parsley. Taste and adjust seasoning, if necessary.
Drizzle each bowl with pesto, Parmesan and serve with crusty bread.