Light the Artisan Fire Pizza Oven, setting the bottom burner to high, and the back burner to just above low. (This will maintain an oven temperature of about 425°F.) While the oven is preheating, place the mushrooms and onions in a large mixing bowl. Drizzle with olive oil and toss to coat them.
Then, season with the remaining ingredients, and toss again until the mushrooms and onions are evenly coated. Transfer them to a parchment lined baking sheet and place in the oven on a wire cooling rack for 15 minutes, rotating the baking sheet 180° after seven minutes.
While the mushrooms and onions are roasting, add all the pasta ingredients (except the pecorino cheese) to a large mixing bowl. When the mushrooms and onions are finished, remove from the oven.
Add them to the mixing bowl with the other pasta ingredients. Stir until well combined. Transfer the mixture into an oven safe cooking vessel, and cover with foil. Place it in the Artisan Fire Pizza Oven on the wire cooling rack and allow it to bake for 20-25 minutes. Remove from the oven, and adjust the main burner to high and the bottom burner to off. Remove the foil from the pasta, top with pecorino cheese and return to the oven for five minutes, or until the cheese has melted and the pasta just starts to char on the edges.
Remove from the oven and serve hot.
