In a large pot, heat olive oil. While oil is heating, chop veggies.
Sauté garlic, onions, carrots, and celery until onions are translucent, about 10 minutes.
While veggies sauté, chop ham/potatoes and gather other ingredients.
Add all remaining ingredients to the pot, except milk and peas
Bring the soup to a boil. Allow it to boil for 10-12 minutes, or until your potatoes are fork tender.
Once cooked, reduce heat and stir in milk and peas.
For thickening: The soup will thicken as it cools, but if you prefer a richer, thick soup - add ¼ cup all purpose flour to a bowl. Scoop 1-2 cups of broth (it’s ok if a few veggie/ham pieces get in there too) into the bowl. Whisk together. Add flour mixture back into the soup and stir. Bring to a boil for 2-3 minutes and your soup will naturally thicken.