Cook the pasta Cook the penne pasta according to package directions. Before draining, reserve about 1 cup of the pasta water. Drain the pasta and set aside (do not rinse).
Cook the mushrooms In a large skillet, heat 1 tablespoon of olive oil over medium heat. Add the sliced mushrooms along with a pinch of salt and pepper. Add about 1/4 to 1/2 cup of water to help keep the mushrooms from drying out while they cook. Sauté until tender.
Add the chicken Stir in the shredded rotisserie chicken and cook until warmed through. Remove from heat.
Combine everything Add the cooked pasta to the skillet and stir to combine with the chicken and mushrooms. Add the spinach artichoke dip and mix until everything is evenly coated.
Adjust the sauce Pour in 1/2 to 1 cup of the reserved pasta water, a little at a time, until the sauce reaches your desired consistency.
Assemble and bake Transfer the mixture to a casserole dish and top with shredded mozzarella cheese.
Bake at 350°F for about 20 minutes, or until the cheese is melted and bubbly.