Melt butter in a soup pot over medium-high heat. Add onions and sauté until tender.

Add mushrooms and cook until tender, stirring as needed.

Add 1 cup of broth to deglaze, then stir in thyme.

In a bowl, whisk flour and remaining broth until smooth. Add to the pot, stirring constantly, and bring to a boil.

Stir in milk or cream, reduce heat, and simmer uncovered for 10 minutes until thickened.

Season with salt and pepper. Serve warm, garnished with fresh parsley.