First prep the leeks: Chop the dark green parts off of the leeks, along with the white ends. Slice the leeks vertically in half. Place in a strainer and run water through the leeks, peeling back layers with your hands to wash off any excess dirt that's hiding in the leeks. Transfer to a cutting a board and thinly slice the leeks.
Warm the olive oil in a pot over medium-low heat.
While the olive oil is warming, mince the onion and garlic.
Cook the leeks and white onion in the olive oil for 5 minutes. Add the garlic, stir, and cook for another 3 minutes.
Meanwhile, peel the potatoes and chop them into bite-sized cubes.
Add the potatoes to the pot and bring the heat up to high. Pour in the broth, and bring the mixture to a boil.
Cover, lower the heat down to medium for a low simmer, and cook for 15-20 minutes until the potatoes are tender.
Meanwhile, dice the zucchini.
Use an immersion blender to process the soup into a smooth and creamy mixture with few potato cubes. Option to transfer the soup into a food processor or blender, and blend the soup that way instead.
Add in the diced zucchini, ditalini pasta, salt, pepper and thyme. Simmer for another 10 minutes, or until the pasta is cooked al dente.
Spoon into bowls, add chopped chives on top, and enjoy! Dip crusty bread into the soup for some extra yumminess.