Bring a large pot of water to a boil. Add penne and cook, stirring occasionally, until tender yet firm to the bite, about 11 minutes.
Meanwhile, whisk 1/2 cup broth, sour cream, flour, mustard, salt, thyme, and 1/4 teaspoon pepper together in a small bowl.
Heat 1 tablespoon oil in a large nonstick skillet over medium-high heat. Add Goolsby’s Sausage; cook until browned on all sides, about 5 minutes. Transfer to a bowl. Drain pasta and keep warm.
Heat the remaining oil in a skillet over medium-high heat. Add mushrooms, broccoli, and onion. Cook, stirring occasionally until vegetables are lightly browned and crisp-tender, 5 to 7 minutes. Return Sausage to the skillet. Add remaining broth. Bring mixture to a simmer.
Reduce heat to medium. Stir the sour cream mixture into the skillet. Cook, stirring frequently, until thickened and bubbly. Gently simmer for about 2 minutes more.
Serve sausage and vegetable mixture over pasta and sprinkle with parsley and additional black pepper.