In a large skillet, melt butter with olive oil over medium heat. Add onion, carrot, celery, and mushrooms. Cook 6–7 minutes until softened. Add garlic and cook 1 more minute.
Sprinkle flour over vegetables. Stir well and cook for 1–2 minutes to remove raw flour taste.
Slowly whisk in stock, followed by milk. Stir constantly until the mixture thickens (about 5 minutes).
Add thyme, bay leaf, salt, and pepper. Reduce the heat to low and simmer for 10 minutes.
Stir in cooked turkey. Simmer gently 5–7 minutes until heated through.
Remove bay leaf. Taste and adjust seasoning. Garnish with parsley before serving.
Notes
Substitute chicken if no turkey is available.
To lighten it up, use low-fat milk and less butter.
To make gluten-free, replace flour with cornstarch slurry (1 tbsp cornstarch mixed with 2 tbsp cold water).