Cook the penne pasta according to package instructions until al dente. Drain and set aside.
Heat olive oil in a large skillet over medium-high heat. Add the chicken thighs, season with salt and pepper, and cook until golden and cooked through, about 6-8 minutes. Remove chicken from skillet and set aside.
In the same skillet, add butter and sliced mushrooms. Sauté until mushrooms release their liquid and start to brown, about 5 minutes.
Add minced garlic and cook for another 1 minute until fragrant.
Pour in the chicken broth and heavy cream, then stir in dried thyme. Bring to a gentle simmer and cook for 3-4 minutes to slightly thicken the sauce.
Return the cooked chicken to the skillet and stir to coat with the sauce. Adjust seasoning with salt and pepper as needed.
Add the cooked penne pasta to the skillet and toss everything together until well combined and heated through.
Remove from heat and stir in grated Parmesan cheese until melted and creamy.
Garnish with chopped fresh parsley if desired and serve immediately.