Heat the oil in a large saucepan or small soup pot. Add the carrots and potatoes and 1 cup water. Bring to a rapid simmer, then lower the heat and cook for 5 minutes.
Add the green beans, alphabet noodles, broth, tomatoes, dill, and paprika. Return to a simmer, then cook gently, covered, for about 15 minutes, or until the vegetables and noodles are tender.
Add the peas and simmer for just a couple of minutes longer. Add a little more water if the broth seems crowded and cook just until heated through.