In a large stock pot or dutch oven, heat oil over medium-high heat. Once the oil is hot, add onions and cook for about 5 minutes. Add garlic and cook for another minute or so. Making sure not to burn the garlic.
Add the potatoes, chicken broth and water. Bring to a boil. Reduce heat to medium and cook for about 20 minutes, or until the potatoes are fork tender.
Remove 2 cups of potatoes with a slotted spoon and set aside. With a masher, mash remaining potatoes right in the pot.
Once the potatoes are mashed, whisk in milk, sour cream, cheese, dried parsley, salt and pepper.
Stir in reserved cubed potatoes and bring to a light boil.
Whisk together the corn starch and water. Pour mixture into boiling soup and reduce heat to a low simmer. Simmer for another 5 minutes, until slightly thickened.
Garnish soup and enjoy!