Melt butter in a large saucepan over medium heat. Add mushrooms and shallots, and saute until mushrooms have softened, 3 to 5 minutes. Stir in garlic, and cook for about 30 seconds.
Add flour and stir constantly for about 2 minutes. Gradually pour in chicken broth, half-and-half, and sherry. Bring to a simmer, stirring often.
Reduce heat to low, stirring occasionally until soup starts to slightly thicken, about 10 minutes. Add Cheddar and Boursin, and stir just until cheese has melted. Season with salt and pepper.
Sprinkle with parsley to serve.