Cook the pasta according to package directions in lightly salted water. Drain and set aside.
Sprinkle the chicken with salt and pepper. Heat the butter and olive oil over high heat in a large skillet. Add the chicken chunks in a single layer and do not stir for a minute or two in order to allow the chicken to brown on the first side. Flip the chicken and brown on the other side. Cook until done, and then remove the chicken from the skillet.
Turn the heat to medium. Add the garlic and quickly stir to avoid burning. After about 30 seconds, pour in the broth and wine, stirring to deglaze the skillet. Allow the liquid to bubble up, and then continue cooking until it's reduced by at least half (most of the surface of the liquid should be bubbling at this point).
Turn off the heat. Add the spinach, tomatoes, chicken, cooked pasta and Parmesan shavings to the skillet. Toss to combine; the spinach will wilt as you toss everything.
Add more Parmesan shavings and serve immediately! Serve with extra Parmesan shavings.