Add butter and olive oil to a Dutch oven and cook over medium heat until melted.
Add onions, celery, and carrots. Cook until softened, about 3 minutes. Add garlic, thyme, dry mustard, and red pepper flakes, and cook for a minute or two.
Add the flour and combine with the vegetables. Cook for a couple of minutes to eliminate the raw flour taste and the flour is incorporated.
Slowly add the chicken stock a little at a time, stirring constantly until the stock thickens a little.
Add the raw chicken breasts. If using cooked chicken, it will be added later.
Simmer the soup and when the chicken breast is thoroughly cooked remove it from the pot and set aside to cool. Dice or shred.
Add the cream to the soup and gently simmer. Do not boil.
When the soup simmers, add the gnocchi. Add the chicken.
Gently simmer the gnocchi for 3 or 4 minutes. Do not boil.
Add the spinach and simmer for another 3 minutes.
Serve. Sprinkle with Parmesan cheese, if desired.