In a large, heavy pot, melt 4 tablespoons of butter over medium heat.
Add the sliced mushrooms with two generous pinches of salt, tossing them to coat. Cook the mushrooms, stirring occasionally, for about 25-30 minutes until their liquids have evaporated and they develop a deep, golden-brown color. Stir more frequently towards the end to avoid burning.
Stir in the chopped onions and cook for an additional 3 minutes, stirring occasionally. Follow with the minced garlic, cooking for 2 more minutes while stirring frequently.
Incorporate the remaining 2 tablespoons of butter, allowing it to melt completely. Add the flour, stirring constantly while scraping the pot's bottom, and cook for 1-2 minutes until the raw flour scent dissipates.
Pour in the dry white wine, scraping the browned bits off the pot's base to deglaze and enhance the soup’s flavor. Stir well.
Gradually add the chicken broth while stirring continuously. Toss in the parmesan rind and thyme, then season with salt and black pepper according to your preference.
Reduce the heat to low and cover the pot. Allow the soup to simmer gently for 20-30 minutes, stirring occasionally to ensure the flavors meld beautifully.
If a thicker consistency is desired, stir in the cornstarch and water mixture during the last minute of cooking.
Remove the pot from the heat and blend in the heavy cream and lemon juice, stirring until well combined.
Serve the soup warm, garnished with grated parmesan, sautéed mushrooms, and chopped parsley, if desired.