Place the cooked ground turkey into the slow cooker with the garlic, carrot, mushrooms, corn, and peas. In a small bowl, whisk together the broth, tomato paste, soy sauce, and oregano. Pour over the meat and vegetables. Cover and cook on high for 2 hours or low for 4 hours.
Meanwhile, Place the potatoes in a large soup pot and cover with water. Bring to a boil for about 10 minutes or until tender.
Drain and place the potatoes in a large bowl and mash until mostly smooth with the skim milk.
After the cook time is complete for the meat and vegetables, skim off any excess liquid. Spread the mashed potatoes on top of the meat mixture in an even layer and sprinkle cheese on top. Cover and cook another 20 minutes on high.