Heat 1 tablespoon butter in a Dutch oven or soup pot over medium heat until melted, then swirl to coat the bottom of the pot. Add onion, carrots, and celery and saute for eight minutes, stirring occasionally, until veggies are softened.
Stir in 1 tablespoon butter, mushrooms, and garlic. Continue to saute over medium heat for another five minutes, stirring occasionally, until mushrooms are softened and browned.
Stir in the flour, sea salt, and pepper and continue to cook for another one minute, stirring often.
Gradually stir in the broth.
Add the turkey, bay leaf, thyme, and smoked paprika, then bring the pot to a boil. Reduce heat to medium low and simmer for 15 minutes, stirring occasionally.
Remove and discard the bay leaf. Stir in milk until heated through, about 5 minutes, then serve.
Notes
You can optionally top your soup with chopped green onion as shown here — and can double the mushrooms, if you want an extra mushroom-y punch!