Melt 4 Tbsp butter in a heavy pot over medium heat.
Add mushrooms and two pinches of salt and toss. Let cook tossing occasionally, until liquids have evaporated and mushrooms have browned, about 25 to 30 minutes (toss more frequently near the end of cooking to prevent burning).
Add onions and saute 3 minutes longer, tossing occasionally. Then add garlic and cook 2 minutes longer, tossing frequently.
Melt in remaining 2 Tbsp butter then add flour and cook 1 to 2 minutes while scraping bottom of pot and tossing constantly.
Pour in white wine and scrape up browned bits from bottom of pot and stir mixture.
While stirring, slowly pour in chicken broth. Add parmesan rind and thyme. Season with salt and pepper to taste.
Reduce heat to low and let gently simmer for 20 to 30 minutes, covered. Stir occasionally.
If you'd like to thicken soup more add cornstarch water mixture during the last 1 minute of cooking.
Stir in heavy cream and lemon juice and remove from heat.
Serve with optional garnishes of parmesan, sauteed mushrooms and parsley.