Prepare wild rice, according to package instructions.
Add 2 Tbsp butter to a large heavy bottomed deep pot and heat over MED-HIGH heat. I use my dutch oven for this. When melted, add sliced mushrooms and cook, about 6-8 minutes, until mushrooms are golden brown. Remove to a plate.
Add last 2 Tbsp of butter to the pot, along with the onions, carrots, and celery. Cook for 4-5 minutes, stirring every so often, until soft. Add garlic and cook until fragrant, about 30 seconds.
Add in all the seasonings (salt, pepper, thyme, rosemary, sage and marjoram - if using), and the flour. Stir well and cook about a minute to get rid of that raw flour taste.
Return about 2/3 of the cooked mushrooms back to the pot, reserving the last 1/3 for topping the soup with later. Add in shredded or cubed chicken.
Pour in the chicken stock, milk, and half and half (or heavy cream), and stir well. Bring to a boil over HIGH heat, then once boiling, reduce heat to LOW and simmer, covered, for 15-20 minutes.
Add in cooked rice and stir to combine. Add lemon juice, stir, and taste. If desired, add additional salt and pepper, to your tastes. Remove bay leave and serve hot, topped with reserved cooked mushrooms.
This soup is amazing served with slices of toasted crusty bread!