Bring a large pot of salted water to a boil. Add penne pasta and cook until al dente, about 8-10 minutes. Add broccoli during the last 2 minutes of cooking. Drain and set aside.

In a large skillet over medium heat, melt the butter. Add the sliced kielbasa and cook for about 5 minutes until lightly browned.

Stir in diced onion and minced garlic. Cook for 2-3 minutes until the onion softens.

Whisk together cornstarch and milk until smooth. Pour into skillet, stirring continuously. Simmer for 3-5 minutes until sauce thickens.

Reduce heat to low, stir in shredded cheese until melted and combined into the sauce.

Add pasta and broccoli to the skillet and gently toss until coated with the sauce. Season with salt and pepper.

Garnish with freshly chopped parsley and serve hot.