Cook Veggies. In a large Dutch oven or soup pot, heat the olive oil over medium heat. Add onion, carrots, celery, and potatoes and cook veggies 12-15 minutes, or until almost fork-tender.
Build Flavor. Add garlic, salt, pepper, rosemary, thyme, and sage. Stir and cook 1 minute. Add chicken broth and cover the pot.
Simmer. Bring soup to a simmer over medium-high heat, then reduce heat to medium and simmer 10-15 minutes or until the potatoes are just cooked through. (They shouldn't be mushy but shouldn't be hard).
Thicken. Remove 1-1 1/2 cups of the veggies and broth mixture and transfer to a high-speed blender with the coconut or almond milk. Blend until completely smooth and pour back into the soup pot with the remaining veggies and broth.
Finish. Stir through to combine, and add cooked chicken and frozen peas. Cook 1-2 minutes more, then garnish with fresh herbs. Taste, and add additional salt, pepper, or herbs, as desired.
Serve & Store. Enjoy right away, and store leftover soup in an airtight container in the refrigerator 2-3 days.