Preheat the oven to 425° Fahrenheit. Cook the chicken breasts on a baking sheet for 25 - 30 minutes, until cooked through. Once cooled, shred the chicken. (To save time, you can also skip this step and use about 4 cups pre-cooked chicken or rotisserie chicken, shredded). 

Add the butter to a large pot or dutch oven over medium heat. Once melted, cook the onion 3 - 4 minutes, until translucent. Add the garlic and cook for 1 minute more. 

Add the broth and diced potatoes to the pot. Bring to a boil and then turn the heat down to simmer, covered, for 15 - 20 minutes, until the potatoes are tender. Stir occasionally. 

Add half of the potatoes (along with some of the onion and garlic) with 2 cups of milk to a blender or food processor and blend until smooth. You can also mash the potatoes by hand, but the texture will not be as creamy.

Add everything to the pot, including the pureed potatoes, shredded chicken, and remaining ingredients: frozen vegetables and seasonings. Simmer over medium heat for 10 minutes, uncovered, and stirring frequently so that the soup does not stick to the bottom of the pot. 

Taste and season with additional salt and pepper if preferred. Serve warm, optionally topped with fresh parsley and a side of bread, biscuits or crackers.