Bring a large pot of salted water to a boil and cook the pasta shells according to package instructions until al dente.
While the pasta cooks, heat butter and olive oil in a large skillet over medium-high heat.
Add the sliced mushrooms to the skillet and sauté for 5 to 7 minutes until browned and moisture has evaporated.
Stir in the minced garlic and thyme, cooking for 1 minute until fragrant.
Pour in the broth to deglaze the pan, scraping up any browned bits from the bottom.
Reduce heat to medium-low and stir in the heavy cream. Simmer for 3 to 4 minutes until the sauce slightly thickens.
Reserve 1/2 cup of pasta water, then drain the pasta shells.
Add the cooked shells and Parmesan cheese to the skillet, tossing to coat thoroughly.
Adjust the sauce consistency with the reserved pasta water if necessary.
Season with salt and pepper, garnish with fresh parsley, and serve immediately.