Bring a large pot of salted water to a rolling boil. Cook the rigatoni until just shy of al dente (about 10 minutes). Reserve 1/2 cup of starchy pasta water, then drain.

In a large deep skillet, heat olive oil and 1 tablespoon butter over medium-high heat. Add sliced mushrooms in an even layer and sear undisturbed for 3-4 minutes until deeply golden brown.

Stir mushrooms and sauté 3 more minutes. Reduce heat to medium, add minced garlic, remaining butter, and fresh thyme; cook 60 seconds until fragrant.

Pour in vegetable broth to deglaze the skillet, then pour in heavy cream. Bring to a gentle simmer for 3 minutes until slightly thickened.

Add cooked rigatoni directly to the skillet along with freshly grated parmesan and 2-3 tablespoons reserved pasta water. Toss vigorously for 1-2 minutes until sauce turns glossy and clings to every ridge.

Season with kosher salt and cracked black pepper. Garnish with extra parmesan flakes and fresh thyme sprigs before serving immediately.