Melt butter over medium-high heat in a medium-large saucepan. Stir in mushrooms, spring onions, garlic and tarragon. Cook until fragrant and mushrooms are softened.
Stir in flour — to create a roux — until mixture has thickened. Stirring constantly, slowly mix in the broth.
Bring soup to a low boil, then lower to medium heat and simmer for 10 minutes. Add salt and pepper, to taste.
Berfore serving, stir in 2 teaspoons heavy cream per bowl. Top with chopped fresh parsley for garnish.