Bring about 2-2.5 quarts of water to boil and add turkey breasts. Lower the heat to medium-low, add bay leaf, and season with salt and pepper. Cook for an hour an a half. Take the pot off heat, take out the turkey, and set it aside to cool down. Once turkey is cooled enough to be handled, dice both turkey breasts into small cubes.
Transfer the broth into another container and use the same pot to make the soup as you used to make the broth.
Set heat to medium-high and add a couple of tablespoons of oil to the pot.
Add diced onions and carrots to the pot and saute for a few minutes, until golden.
Add garlic and cook until fragrant.
Lower the heat to medium.
Add diced potatoes and cook for a few minutes.
Add diced turkey to the veggies. Mix and cook for a few minutes.
Start pouring in turkey broth and stirring. Add enough turkey broth to cover the vegetable mixture well (about 1/4 inch above the turkey and veggie mixture).
Season with more salt and pepper if needed.
Lower the heat to medium-low and cook until potatoes are tender.
Once potatoes are tender, stir in heavy whipping cream and freshly grated Parmesan cheese. Cook for a few more minutes and take off heat.
Top off with some more Parmesan cheese when serving.