Heat a large stockpot over medium-high heat. Add butter. Once melted add onions and cook 3-5 minutes until soft. Then add garlic and cook until fragrant, about 2 minutes.
Add flour and stir to combine—cook for 2 min. Then add in vegetable stock slowly, whisking until smooth. Continue to add half-n-half, milk, potatoes, salt, pepper, garlic powder, dried mustard, and thyme. Stir well.
Slowly bring the soup to a low boil—don't let it rapidly boil—then reduce the heat to low, and let simmer for 20 min. Once done, turn off the heat and add the cheese and sour cream. Remove from the heat, cover, and let sit for 15 minutes, to macerate. Taste for salt and adjust if needed. I usually sprinkle in a good finger pinch extra. Serve warm, topped with sliced chives, or just add all the chives into the soup.