Cook the noodles according to the package directions until they are al dente.

Meanwhile, in a large heavy skillet, heat the oil over medium heat.

Add the garlic, mushrooms, and thyme and sauté them for 1 minute.

Add the broth and simmer it over medium-low heat, stirring occasionally, until the noodles are ready.

When you add the pasta to the boiling water, add the peas and salt to the mushroom mixture.

When the penne is cooked, drain it briefly, allowing some water to cling to the noodles, and return it to the warm pot over low heat.

Add the mushroom-pea mixture and the Parmesan cheese and stir it until it is heated through.

Serve it immediately, topped with additional Parmesan cheese, or refrigerate it for up to 2 days.