Bring a large pot of salted water to a boil. Cook the penne according to package directions, reducing the suggested time by 1 minute so the pasta is slightly underdone. Drain and set aside.
Heat a large skillet over medium heat and add 1 tablespoon of the oil from the sun-dried tomato jar. When hot, add the sliced mushrooms and cook, stirring occasionally, about 3 minutes.
Add the chopped sun-dried tomatoes to the mushrooms and cook 1–2 more minutes, until mushrooms are tender. Remove the mixture from the pan and set aside.
Return the pan to medium-high heat. Add another tablespoon of sun-dried tomato oil and the butter. When the butter melts, add the minced garlic and sauté about 30 seconds until fragrant.
Sprinkle the flour over the butter and garlic and whisk constantly for about 1 minute to cook the flour and prevent lumps.
Gradually whisk in the chicken stock, then the milk, whisking constantly to combine. Bring the mixture to a boil, then reduce heat to medium-low and simmer until the sauce thickens, stirring occasionally.
Reduce heat to low and stir in the Italian seasoning and 5 tablespoons of grated Parmesan until the cheese melts. Season the sauce with salt and pepper to taste.
Add the drained pasta, cooked mushrooms and sun-dried tomatoes, diced chicken, and spinach to the sauce. Toss over medium heat until everything is coated and the spinach wilts, about 1–3 minutes.
Remove from heat, sprinkle 1/2 cup grated Parmesan over the pasta, give a final stir, and serve immediately garnished with fresh thyme if desired.