Preheat oven to 375ºF. Spray a large nonstick skillet with cooking spray and set it over medium heat. Add the ground turkey, onions, mushrooms, salt, and pepper, and cook, crumbling the turkey with a wooden spoon as you go, until the turkey is browned, about 8 minutes. Add the garlic and cook, stirring constantly, until fragrant, 30 seconds.
Add the crushed tomatoes and 2 teaspoons of the oregano. Bring the pan to a simmer. Reduce the heat to low and simmer for 10 minutes. Remove from heat and set aside.
In a large bowl, combine the ricotta with the remaining teaspoon of oregano, and the basil. Stir to mix well.
Spray a standard-size muffin tin with cooking spray and place 1 wonton wrapper in each of the 12 cups, pressing firmly in the bottom of the cup and up the sides. Using half of the ricotta mixture, divide it among the 12 muffin cups. Next, using half of the turkey tomato sauce, spoon it evenly over each of the ricotta filled cups. Sprinkle with 2 teaspoons of the mozzarella. Gently press another wonton wrapper on top of the mozzarella layer. Repeat the layering process, finishing with mozzarella cheese. Bake until the wonton edges are crispy and the cheese has melted, 10 to 12 minutes.
Let the cups cool, remove them from the pan, and serve!