In a large pot, heat 2 tablespoons of butter and 1 tablespoon of olive oil over medium heat. Add diced onion and sauté for 3-4 minutes until translucent. Stir in minced garlic and fresh thyme, cooking for an additional 1-2 minutes until fragrant.

Add 1 pound of sliced mushrooms to the pot, stirring frequently. Sauté for about 8-10 minutes until soft and browned. If using white wine or sherry, deglaze the pot by adding a splash now.

Optional: Sprinkle in 1 tablespoon of all-purpose flour over the cooked mushrooms. Stir well for 1-2 minutes to cook off the raw flour taste.

Pour in 4 cups of vegetable or chicken broth, stirring to combine. Increase the heat to bring to a gentle simmer, cooking uncovered for about 10-15 minutes.

Remove from heat and use an immersion blender to achieve a smooth consistency, or blend in batches using a countertop blender and return to pot.

Stir in 1 cup of heavy cream or half-and-half, heating through on low for an additional 3-5 minutes. Adjust seasoning with salt and pepper.

Ladle the soup into bowls and garnish with fresh chopped parsley. Serve with warm, crusty bread.