Add mushrooms, onion, garlic, broth, thyme, salt, and pepper to the slow cooker.
Cook on low for 4–5 hours or high for 2–3 hours, until mushrooms are soft.
In a small pan, melt butter over medium heat. Whisk in flour and cook 1 minute.
Stir in half-and-half slowly until smooth. Heat until slightly thickened.
Pour the cream mixture into the slow cooker and stir well. Cook 15–20 more minutes.
Taste and adjust salt. Stir in parsley if using. Blend some soup with an immersion blender for creamier texture.