In a large skillet, heat a tablespoon of olive oil over medium-high heat. Add the sliced kielbasa and cook for 4-5 minutes until browned. Remove kielbasa and set aside.

In the same skillet, add more olive oil if needed, then toss in the broccoli florets. Sauté for 3-4 minutes until bright green and slightly crunchy.

Add the minced garlic to the skillet and sauté for another minute until fragrant.

Pour in the heavy cream and chicken broth, scraping the bottom to deglaze. Stir in Italian seasoning, salt, and pepper, and bring to a gentle simmer.

Sprinkle in the shredded cheddar cheese, stirring continuously until it melts smooth into the sauce.

Return the seared kielbasa to the skillet, stirring to coat in the cheese sauce, and warm everything through for 2-3 minutes.

Stir in the butter until melted for a glossy finish.

Reduce heat to low and let simmer for another 2-3 minutes. Serve hot, garnished with additional cheddar if desired.