In a large pot, melt 3 tablespoons of butter over medium-high heat. Add 1 diced onion and sauté for about 3-5 minutes, stirring frequently, until the onions become tender and translucent.

Stir in 8 ounces of sliced mushrooms and continue to cook for 5-7 minutes until they soften and turn golden brown.

Add a splash of vegetable broth to the pot, scraping up any browned bits stuck to the bottom with a wooden spoon.

In a separate bowl, whisk together ¼ cup of all-purpose flour and the remaining vegetable broth until smooth. Slowly pour this mixture into the pot while stirring continuously to prevent lumps from forming.

Bring the mixture to a gentle boil over medium heat, then reduce heat to low and let it simmer for 10-15 minutes.

Stir in 1 cup of milk or heavy cream and season with salt and pepper to taste. Keep the soup over low heat for a few more minutes, warming it through without boiling.

Ladle the warm soup into bowls and garnish with freshly chopped parsley.