In a large pot, sauté the sliced sausage over medium heat until browned.
Add the chopped onion and cook until translucent.
Stir in the minced garlic and cook for an additional minute.
Add the diced potatoes and sliced carrots to the pot.
Pour in the chicken broth and bring to a boil.
Reduce heat to a simmer and cook until the vegetables are tender, about 15 minutes.
Stir in the milk and season with salt and pepper.
Allow the soup to heat through without boiling.
Remove from heat and let sit for a few minutes.
Serve hot, garnished with fresh parsley.