Bring a large pot of water to a boil. Add the cabbage leaves and return to the boil. Cook until cabbage is pliable, about 8 minutes; drain. Rinse the cabbage under cold running water; drain and transfer to a cutting board. Trim the thick ribs from the base of the leaves and discard.

Preheat oven to 350°F. Spray a 9 x 13‑inch baking dish with nonstick spray.

Heat oil in a large nonstick skillet over medium-high heat. Add mushrooms and onion and cook, stirring occasionally, until tender, about 8 minutes. Transfer mushroom mixture to a large bowl. Stir in ground turkey, rice, egg whites, and salt until well mixed.

Place 1/8 of the filling in the center of one cabbage leaf. Fold in the sides of the leaves over the filling and roll up. Repeat with the remaining filling and cabbage.

Spread about 1/2 cup of marinara sauce on the bottom of the baking dish. Put the cabbage rolls, seam-side down, in the baking dish. Stir together remaining marinara sauce, water, and vinegar in a medium bowl; pour over the rolls. Cover and bake until cabbage is very tender and the sauce is bubbly, about 1 1/2 hours.