In a large skillet, heat 2 tablespoons of extra-virgin olive oil over medium heat. Add the sliced shallots and a pinch of kosher salt. Sauté for 3-4 minutes until they soften and turn translucent.

Add the sliced portobello mushrooms and cook undisturbed for about 4-5 minutes. Sprinkle with salt and continue cooking until tender.

Bring a pot of salted water to a boil. Add the pappardelle pasta and cook according to package instructions, usually about 3-5 minutes for fresh pasta. Reserve 1 cup of pasta water before draining.

In the skillet, add rosemary, garlic, chili flakes, tomato paste, butter, and balsamic vinegar. Stir for 2-3 minutes until the garlic softens and flavors meld. Gradually pour in reserved pasta water until a glossy sauce forms.

Add the drained pasta to the skillet and toss to coat with the sauce. Add more pasta water as needed for desired consistency.

Plate the pasta into shallow bowls and top with grated Parmigiano Reggiano or Parmesan cheese. Serve immediately.