Spray slow cooker with non-stick cooking spray, set aside.
In a small bowl, mix together the goat cheese, egg, and oregano to form the cheese mixture.
Place 2 T of pasta sauce in the bottom of the slow cooker pot. Sprinkle half of the zucchini and half of the shredded carrot over sauce and top with 1/3 cup of the cheese mixture. Break two noodles into pieces and cover the cheese.
Create the second layer the same way: 2 T of pasta sauce, the rest of the zucchini and shredded carrot and top with 1/3 cup of the cheese mixture. Break two noodles into pieces and cover the cheese.
Continue with the layers: Spread 2 T of sauce and then layer half of the spinach, and half of the mushrooms, top with some cheese mixture and broken noodles. Repeat layering with the remaining spinach and mushrooms, ending with cheese, and the remaining sauce.
Firmly press all the ingredients into the slow cooker pot. Cover and cook on the high heat setting for 4-5 hours. Allow lasagna to rest 20 minutes before cutting into wedges. Serve with a little extra sauce and top with chopped fresh basil.