In a large skillet over medium high heat, heat 2 Tablespoons of the olive oil. Add the oyster mushrooms, season with kosher salt, and sauté for about 6 minutes, stirring often, until they are soft and golden brown.
Meanwhile, brush remaining olive oil evenly over naan bread. Then top each piece with ¼ cup of the shredded mozzarella cheese and 2 Tablespoons of Parmesan, leaving a 1-inch crust around the edges. Sprinkle each with ⅛ teaspoon of Italian seasoning and ¼ cup of the roasted red peppers.
Remove cooked mushrooms from the skillet and transfer to a plate.
Place naan bread on a rimmed baking sheet and bake in the preheated oven for 3 minutes.
Meanwhile, in the same skillet, add chopped spinach and minced garlic and sauté for 2 minutes over medium-high heat.
Remove naan from the oven and top with cooked mushrooms and spinach. Place it back in the oven and bake for 3 minutes more. Slice and serve.