Melt butter in a soup pot and cook onion, celery and carrot over medium heat for 6 minutes.
Add potatoes, chicken, broth, salt and garlic powder. Simmer gently for 18 to 22 minutes until the potatoes are tender and the chicken reaches 165°F.
Put cream cheese in a heatproof bowl and whisk in 1 cup hot broth a little at a time until smooth.
Stir the cream cheese mixture back into the pot with milk, hot sauce and dried dill. Heat gently for 2 to 3 minutes without boiling hard.
Let stand off the heat for 2 minutes, stir once and serve with the chicken and potato pieces evenly divided.