In a large pot heat the olive oil over medium heat. Add the diced onion, celery and leeks. Season with salt. Cook for about ten minutes.
Fill the pot with the vegetable broth and bring to slight boil.
Bring down the temperature, add the pasta, cannellini beans, peas, snap peas and spinach. Simmer everything until the pasta is cooked al dente. Season the minestrone with salt and pepper to taste.
Serve the minestrone in a bowl, with dollops of pistachio pesto and shavings of parmesan cheese.