Preheat the oven to 375 degrees F (190 degrees C). Spray a 1 1/2-quart souffle or other baking dish with cooking spray.
Melt butter in a large, nonstick skillet over medium heat until bubbly. Add onion and cook until it begins to turn translucent, 2 to 3 minutes. Add mushrooms and cook until they begin to soften and release a little moisture, about 4 minutes. Stir in garlic and cook until fragrant, 1 to 2 minutes.
Stir in Italian seasoning, salt, pepper, sage, paprika, and cayenne. Stir in spinach and parsley; cook until spinach is just wilted, about 1 minutes. Add flour and stir until flour is coated in butter and seasonings; continue to cook and stir for 2 minutes. Stir in frozen vegetables and vegetable broth; bring to a boil. Cook until mixture begins to thicken, 3 to 4 minutes. Remove from heat and stir in nutritional yeast.
Pour mixture into the prepared dish. Place puff pastry sheet over top, allowing it to drape over the sides of the dish. Use a fork to poke several holes in the top of the pastry, then spray with cooking spray. Place the baking dish on a sheet pan.
Transfer to the preheated oven and bake until the top is nicely browned, 25 to 30 minutes. Allow to cool for about 15 minutes before serving.