In a large pot, heat olive oil or vegan butter over medium-high heat.
Add in celery, carrot, and onion and sauté for 3-5 minutes, or until the onion is translucent.
Pour in vegetable broth, preserving 1 cup for later. Let it come to a boil.
In the meantime, gather a few sprigs of fresh herbs like rosemary, thyme, and sage. Tie them with kitchen twine so you can easily remove them later. (You can also make an herb sachet with a piece of cheesecloth if you like.) If you'd like to sub in dried ground herbs, see the notes.
Place the herb bundle in the soup along with bay leaves. Once the soup comes to a boil, reduce heat to low. Cover and simmer for at least 30 minutes, or up to 2 hours.
When the veggies are as tender as you like, add in your dried pasta. Let it simmer until very al dente — usually about 8-10 minutes depending on your pasta shape. Make sure to stir it every now and then so the pasta doesn't stick together (or to the bottom of the pot).
In the meantime, extract the cloves of roasted garlic from the skins. Place the roasted garlic in a blender along with 1 cup of vegetable broth and blend until smooth. (If you don't want to use a blender, you can also simply chop/mash the garlic into a paste.)
Once the pasta is almost done, pour in the roasted garlic broth (or add the roasted garlic paste with 1 cup veggie broth). Add in your handful of greens. Let the soup keep simmering (just a few extra minutes) until the pasta is fully cooked and the greens are wilted.
Remove the herb bundle/sachet. Squeeze in fresh lemon juice and fresh chopped parsley/dill. Add extra salt and pepper to taste.
Enjoy immediately!