Heat oil in a stock pot until hot but not smoking. Add the onion and garlic, stirring occasionally, until golden, about 3 minutes. Add kale and sauté, stirring 1 minute.
Add frozen vegetables, tomatoes with juice, pasta, broth, water, salt, and pepper and simmer, uncovered, stirring occasionally until vegetables are tender and pasta is al dente, about 10 minutes.
Meanwhile, place half of beans in a wide shallow bowl and coarsely mash them with a fork or a potato masher, then stir mashed and whole beans into soup and simmer, stirring occasionally until soup is slightly thickened, about 5 minutes.
Season with salt and pepper.
A hearty vegetable soup that's a snap to make and so much better than the stuff from a can.