Preheat your oven to 350°F (175°C).
In a cast iron skillet, melt butter over medium heat. Add the diced onion, sliced mushrooms, and chicken base. Sauté for about 20 minutes, until the onion and mushrooms start to caramelize. For deeper caramelization, you can extend this to up to 40 minutes.
Stir in the minced garlic, sage, thyme, and pepper. Cook for an additional minute.
Add the heavy whipping cream and nutritional yeast (if using). Continue stirring occasionally on medium heat until the mixture thickens, which should take about 5-10 minutes.
Fold in the diced turkey, optional parsley, and 1/4 cup of the grated Parmesan cheese. Remove from heat.
If your skillet is not oven-safe, transfer the mixture to an oven-safe baking dish (8" x 8" should be sufficient).
Top with the remaining Parmesan and the mozzarella cheese.
Bake in the preheated oven for 12-15 minutes, or until the dish is bubbly and slightly golden on top. Garnish with additional parsley, if desired, before serving.