Heat oil in skillet over medium high heat in stock pot. Add onion, celery, and carrots and lower heat. Cook until fragrant, about 5 minutes. Add garlic and cook for 2 minutes more. Add salt, pepper, paprika, thyme, and bay leaves and let simmer for 5 minutes.
Keep vegetables in pot but stir in the dry white wine to deglaze the bottom. Cook liquid down to about half..
Stir in the vegetable stock and milk. Add the potatoes and cook until potatoes are tender, about 7 minutes.
Mix the cornstarch and cold milk together making sure to blend until all lumps are gone. Add the cornstarch mixture to the stock pot and stir thoroughly. Simmer for another 5 minutes until the cornstarch flavor is gone.
Add the cubed halibut pieces to the stock pot and let cook at a simmer for 10 minutes or until fish is cooked through. Serve soup with a garnish of parsley, if desired.