Put 2 tablespoons olive oil in a large, deep skillet over medium heat. When hot, add shallot, garlic, and mushrooms. Cook, stirring occasionally, until mushrooms soften and begin to brown on edges, about 10 minutes. Add pasta and cook, stirring occasionally, until it is glossy and coated with oil, 2 to 3 minutes. Add a little salt and pepper, then wine. Stir and let liquid bubble away.
Ladle stock into skillet 1/2 cup or so at a time, stirring after each addition, and every minute or so. When liquid is just about evaporated, add more. Mixture should be neither soupy nor dry. Keep heat at medium and stir frequently.
Begin tasting pasta 10 minutes after you add it; you want it to be tender but with a tiny bit of crunch. When pasta is about 3 to 4 minutes away from being done, add chicken and stir to combine. Continue to cook until chicken is done, it will be white on inside when cut and pasta is how you like it.
Taste, adjust seasoning, garnish with parsley and Parmesan if using, and serve.