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. Cook for about 3–4 minutes until soft and translucent.

Add the sliced portobello mushroom caps to the skillet. Cook for 5–7 minutes until they develop a rich brown color and become tender.

In a large pot, bring salted water to a boil. Cook 8 ounces of pappardelle according to package instructions until al dente, about 4–5 minutes. Reserve ¾ cup of pasta water before draining.

Stir in 1 minced garlic clove, 2 teaspoons of chopped rosemary, and ½ teaspoon of crushed red pepper into the mushrooms. Cook for 1–2 minutes until fragrant.

Mix in 2 tablespoons of tomato paste, 1 teaspoon of balsamic vinegar, and 2 tablespoons of unsalted butter, with ½ cup reserved pasta water to create a thick sauce.

Add the drained pappardelle to the skillet and toss for 2–3 minutes, adjusting with more reserved pasta water if needed. Season with salt to taste.

Plate the dish and garnish with freshly shaved Parmigiano Reggiano cheese. Serve immediately.