Prep the ingredients. Slice mushrooms, dice onion and celery, and mince garlic. If using cooked chicken, shred or cube it now.
If using raw chicken, cut into bite-size pieces and pat dry.
Brown the mushrooms. Heat a large pot or Dutch oven over medium-high. Add olive oil and 1 tablespoon butter. Add mushrooms in an even layer with a pinch of salt.
Cook undisturbed for 3–4 minutes to brown, then stir and cook 3–4 minutes more until golden and reduced. Remove to a bowl.
Sauté aromatics. Lower heat to medium. Add remaining 1 tablespoon butter.
Add onion and celery with a pinch of salt. Cook 4–5 minutes until soft and translucent. Stir in garlic and cook 30 seconds until fragrant.
Add chicken (if raw) and season. If starting with raw chicken, add it now.
Season with salt, pepper, thyme, and parsley. Cook 4–5 minutes, stirring, until the chicken is opaque at the edges. It will finish cooking in the broth.
Build the base. Return browned mushrooms to the pot.
Stir in Dijon, coconut aminos (or tamari), and smoked paprika if using. Pour in chicken broth and add the bay leaf. Bring to a gentle boil, then reduce to a simmer for 12–15 minutes.
Finish with cream. Reduce heat to low.
Stir in heavy cream (and cream cheese if using). Simmer very gently for 3–5 minutes, stirring, until slightly thickened and smooth. Avoid a hard boil after adding dairy.
Add cooked chicken and greens. If using pre-cooked chicken, add it now to warm through for 3–4 minutes.
Fold in spinach or kale and cook until just wilted. Taste and adjust salt and pepper. A squeeze of lemon brightens the richness.
Serve. Ladle into bowls and garnish with fresh parsley or chives.
Crack black pepper on top for a final pop.