Traditionally, minestrone is slow-simmered with Parmigiano-Reggiano rinds to impart a rich umami flavor to the broth. In our shortcut version, soy sauce is used instead, adding instant depth to this pantry-friendly soup.
Add the whole can of diced tomatoes (including the liquid), and bring the mixture to a boil. Stir in the pasta, the white beans and reserved liquid and the soy sauce. Season with salt and pepper. Cook until the pasta is al dente, 7 to 8 minutes, stirring in the green beans during the last 2 minutes of cooking. Serve in individual bowls with a little oil drizzled on top.