In a medium saucepan, heat 2 tablespoons butter over medium-high heat. Add the onion and garlic and cook, stirring, until softened. Add the whole mushrooms and cook, stirring, for 2 to 3 minutes. Add the white wine and simmer until the liquid is reduced by half.
Add the chicken stock and bring to a boil. Reduce the heat and simmer, stirring occasionally, until the vegetables are very tender, about 10 to 15 minutes. Transfer the contents of the pan to a blender and puree until smooth. Return the soup to the pan and bring it to a simmer.
In a small bowl, mash 1 tablespoon butter with the flour. Whisk the flour paste into the simmering soup in increments, until the soup thickens slightly. Continue to simmer the soup, stirring, until no flour taste remains, about 10 minutes. Stir in the cream and return to a simmer. Season with salt and pepper and keep warm.
In a medium saute pan, heat the remaining 2 tablespoons of butter over medium heat. Add the sliced mushrooms and cook, stirring, until lightly softened, about 5 to 7 minutes. To serve, divide the soup among warmed soup bowls. Garnish with the sliced mushrooms, chopped chives and croutons. Serve immediately.