Slice the wild mushrooms into ¼ inch pieces. Peel and roughly chop the garlic, shallot, and parsley. Holding a sprig of rosemary at its top, slide your fingers down the stem to strip off the leaves or needles. Roughly chop the rosemary needles. When the vegetables and herbs are chopped, slice the chicken breasts into ½ inch strips.

In a large pot, bring 3 quarts of water and 1 tbsp of salt to boil. When the water is boiling, add the pasta. Cook the pasta for 5-6 minutes, or until al dente. Strain the pasta and cool with cold running water to stop the cooking process. Let strain and set aside to dry.

Heat a large sauté pan over medium heat and add 1 tsp of olive oil. Season chicken with 1/2 tsp salt and 1/4 tsp pepper, to taste. Add to the sauté pan and cook, stirring occasionally, until just golden, about 3 minutes. Transfer to a bowl with a slotted spoon.

Heat the same sauté pan you used to cook the chicken over medium-to-high heat. Add 1 tbsp. of olive oil and the chopped garlic and shallots to the pan and sauté for 1-2 minutes or until translucent. Add the mushrooms, rosemary, and a pinch of salt and pepper and cook, stirring constantly, until ingredients begin to brown, about 4 minutes. Add balsamic vinegar and cook until reduced by about half. Add the cooked chicken and tomatoes (with juice), then simmer, breaking up tomatoes with a spoon and stirring occasionally, until sauce is just thickened, about 15 minutes. Add the cooked pappardelle and mix together to incorporate ingredients and to warm the pasta. Add salt and pepper, to taste, if needed.

Place pasta mixture in the middle of the plate or bowl, twirling the pasta as you go to build up some height. Sauce the plate with remaining ragù. Garnish with chopped parsley, baby arugula, and sprinkle with parmesan cheese.