In a large skillet, heat the olive oil over medium heat. Add the sausage and cook until browned, breaking it up with a spoon, about 5-7 minutes. Transfer the cooked sausage to a slow cooker.
In the same skillet, add the onion and garlic. Sauté until the onion is translucent, about 3-4 minutes. Add to the slow cooker.
Add the carrots, potatoes, bell pepper, zucchini, diced tomatoes (with juice), vegetable broth, oregano, basil, salt, and pepper to the slow cooker. Stir to combine all ingredients.
Cover and cook on low for 6-8 hours or on high for 3-4 hours, until the vegetables are tender.
About 15 minutes before serving, stir in the frozen peas and let them heat through.
Serve hot, garnished with fresh parsley.