Mix the broth, water, carrots, celery, mushrooms, pheasant, rice (including the seasoning packet) and Lawry’s salt (1 teaspoon or to taste) in the slow cooker.
Cook on low for 6-8 hours or on high for 4 hours.At the end of the cooking time, mix the salt, pepper and flour in a small bowl.
In a medium saucepan over medium heat, melt the butter.
Stir in flour mixture by tablespoon to the melted butter to form a roux (fancy word for thickening agent).
Then, while still on the heat, whisk in the half and half, a little at a time, into the roux until mixed completely and smooth. It will be thick and look a little like smooth mashed potatoes
Stir this mixture into the soup in the crockpot, then let it cook on low for 15 more minutes.
Serve hot in bowls with some crusty bread on the side.