Prepare all ingredients: trim and cut asparagus, slice mushrooms, mince garlic, and cut chicken into uniform bite-sized pieces.

Bring a large pot of salted water to a boil. Cook the penne pasta according to package instructions until al dente. Drain thoroughly and set aside, reserving a small amount of pasta water.

In a large skillet, heat olive oil over medium-high heat. Season chicken with salt and pepper, then sauté until golden brown and cooked through, about 6 to 8 minutes.

Remove cooked chicken from the skillet and set aside. In the same pan, add asparagus and mushrooms. Cook until tender, around 5 minutes.

Add minced garlic to the vegetables and sauté for an additional minute.

Reduce heat to medium and pour in heavy cream, chicken broth, and thyme. Bring to a gentle simmer and cook until the sauce slightly thickens, about 5 minutes.

Return the cooked chicken to the skillet and add the prepared penne pasta. Gently stir to combine and ensure everything is heated through.

Remove from heat and stir in grated Parmesan cheese. If the sauce seems too thick, add a small amount of reserved pasta water to reach desired consistency.