1. 1. Saute the aromatics: 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. 2. Add broth and pasta: Pour in the chicken or vegetable broth and bring it to a gentle simmer. Add the uncooked pasta to the skillet, stirring to ensure it’s submerged in the liquid. Cover the skillet and reduce the heat to medium-low.

3. 3. Cook the pasta: Let the pasta cook for about 10-12 minutes, stirring occasionally to prevent sticking, until it’s almost al dente. The liquid should be mostly absorbed, but there should still be a little left for the sauce.

4. 4. Incorporate the broccoli: Add the broccoli florets to the skillet, stirring them into the pasta. If using fresh broccoli, ensure it’s cut into small, bite-sized pieces for quicker cooking. If using frozen, there’s no need to thaw it first. 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. 5. Create the creamy cheese sauce: Remove the skillet from the heat. Stir in the heavy cream, shredded cheddar cheese, and grated Parmesan cheese. Stir continuously until both cheeses are fully melted and the sauce is smooth and creamy. The residual heat from the pasta and skillet will melt the cheese perfectly.

6. 6. Season and serve: Taste the pasta and season generously with salt and black pepper as needed. Serve immediately while hot and cheesy.