1. Heat the olive oil in a large, deep skillet or Dutch oven over medium heat. Add the chopped onion and cook until softened and translucent, about 3-5 minutes. Stir in the minced garlic and cook for another minute until fragrant, being careful not to burn it.

2. Pour in the chicken or vegetable broth. Bring it to a gentle simmer. Add the uncooked pasta to the skillet, stirring to ensure it’s submerged in the liquid.

3. Cover the skillet and reduce the heat to medium-low. Let the pasta cook according to package directions, or until al dente, stirring occasionally to prevent sticking. This usually takes about 10-12 minutes. The liquid should be mostly absorbed.

4. Once the pasta is nearly cooked, stir in the broccoli florets. If using fresh broccoli, ensure they are cut into bite-sized pieces. If using frozen, add them directly to the pan. Cover again and continue to cook for another 5-7 minutes, or until the broccoli is tender-crisp and the pasta is fully cooked.

5. Remove the skillet from the heat. Stir in the heavy cream, shredded cheddar cheese, and grated Parmesan cheese. Stir continuously until the cheeses are fully melted and the sauce is smooth and creamy.

6. Taste the pasta and season generously with salt and black pepper as needed. If the sauce seems too thick, you can add a splash more broth or milk until it reaches your desired consistency. Garnish with fresh chopped parsley, if desired, and serve immediately.