Heat the oven to 400°F. Choose a baking dish that holds all four mushrooms in one layer.

Wipe each mushroom clean with a damp linen towel. Turn each cap over, push the stem gently to one side until it releases, and reserve all four stems.

Scrape the dark gills from each cap with a stainless spoon and reserve them with the stems. The cavities should look pale tan with shallow scrape marks and no dark radial gill plates. Set the raw caps hollow-side up in the baking dish.

Chop the stems into small pieces. Heat the scaled cooking fat in the skillet over medium-high heat. Add the chopped stems and scaled sea salt and cook for 8 to 10 minutes, stirring often, until softened, darker, and glossy.

Lower the heat to medium-low. Add the reserved gills, scaled garlic, and scaled dried basil and cook for 2 minutes more, until the garlic smells fragrant and the gills have softened without scorching.

Move the mushroom mixture to a medium bowl. Stir in the scaled tomato paste until the sauce is thick, evenly dark brick-red, and free of dry paste streaks. For the nightshade-free version, omit the tomato paste and use the cooked mushroom mixture as the filling.

Divide the sauce among the four mushroom caps. Spread it to the edges without mounding it above the rim.

Top with the scaled or desired amounts of aged cheese, cooked homemade sausage, and sliced brine-cured olives. Keep fresh tomato and fresh herbs for after baking.

Bake for 20 to 25 minutes, until the cheese is completely melted, the surfaces are sizzling, and the mushroom edges are darker and tender. The caps will flatten to varying degrees.

Top with optional fresh tomato and herbs. Lift each pizza from underneath with a wide stainless spatula and serve.