Chop half of the mixed mushrooms finely while slicing the other half of the mushrooms.
In large dutch oven, melt the butter and the oil together over medium heat. Add the shallots, garlic, and mushrooms, and raise the heat to medium high. Saute until the liquid evaporates and the mixture is like a "mush."
Lower heat again to medium, and add the sherry. Stir occasionally and cook until the sherry evaporates.
Add the flour and stiry, cooking about 3 minutes.
Stir in the broth, and raise heat to bring to a boil. Once boiling, reduce heat and simmer for 15 minutes.
Stir in the sour cream and chives, and cook an additional 3 minutes to be sure every thing is heated through.
Turn off heat, add milk, and stir. Add salt and pepper to taste, and serve immediately.