Peel potatoes and dice into large chunks (this helps them cook faster) and chop celery. Add both into soup pot with the chicken broth. Simmer until veggies are tender and potatoes can be easily pierced with a fork, about 25 minutes. While your veggies are simmering, in a separate pan, add the chopped onions along with butter. Cook them very low and slow, stirring frequently so they don't burn or brown, but develop a deep caramel color, for 15-25 minutes. In the last 5 minutes or so, add the chopped garlic, and cook for the remaining few minutes. When your potatoes and celery are done, add the caramelized onions and garlic to the pot, and transfer to a food processor or blender. Blend until smooth. Return blended soup to the pot, and add your milk or cream until the desired thickness and creaminess is achieved (this all depends on preference!) About 2 cups milk or 3/4 cup heavy cream is a good ballpark, but adjust based on preferences! Serve immediately, with parmesan cheese and chopped chives!