Heat 3 tablespoons olive oil in a large pot over medium heat. Add the leeks, celery, yellow squash, and thyme. Cook 2-3 minutes. Stir in the tomatoes and cook 3-4 more minutes; season with salt and pepper.
Add stock or water and bring to a simmer (start with 4 or 5 cups of stock. Depending on how thick you want your minestrone, add another cup if you want it less thick). Cook simmering, covered, for 10 minutes (leave the lid slightly off the pan and keep checking and stirring to make sure it doesn’t boil too much).
If you are adding orzo or a broken pieces of a thin spaghetti, bring soup to a boil and add them in now. When the pasta is almost done, add in the peas. If you aren’t adding pasta to the soup, keep the soup on a simmer and add in the carrots and peas and cook for about 10 minutes (or until the peas are tender).
If you did add the pasta, cook until the pasta is al dente (it will keep cooking in the soup because it is very hot, so check to make sure it doesn’t become too mushy).
Adjust seasonings and serve immediately. Could be served with chopped fresh Italian parsley (leaves only). Garnish with additional thyme (optional).