In a large skillet, heat 2 tablespoons of extra-virgin olive oil over medium heat. Add shallots and kosher salt. Sauté for about 3-5 minutes until soft.

Incorporate sliced portobello mushrooms and cook for 5-7 minutes, stirring occasionally, until golden.

Bring a pot of salted water to a boil. Add pappardelle and cook until al dente, about 7-10 minutes.

Reserve ¾ cup of pasta water, then drain the rest of the pappardelle.

Return to the skillet, add minced garlic, rosemary, and crushed red pepper. Stir in tomato paste and balsamic vinegar, cooking for 2-3 minutes.

Add reserved pasta water to create a sauce, then gently fold in the pappardelle until well-coated.

Serve hot, topped with shaved cheese, if desired.