Note: For best results, use a food processor to finely chop the broccoli into small, even pieces.
Prep Ingredients: Combine the chicken broth, half-and-half, 1/2 bouillon cube, and seasonings in a large measuring cup. Measure out the remaining ingredients before starting.
Sauté Garlic: Melt the butter in a large skillet over medium heat. Add the minced garlic and sauté for 30 seconds until fragrant. Be careful not to burn it.
Make the Roux: Whisk in the flour with the garlic butter and cook for 1–2 minutes, stirring constantly to remove the raw flour taste.
Build the Sauce: Gradually add the chicken broth mixture in small splashes, whisking continuously to avoid lumps. Stir in the broccoli and bring the sauce to a boil, then reduce to a simmer.
Cook the Pasta: Boil pasta in salted water until al dente, then drain.
Finish the Sauce: Reduce the heat of the sauce to low and stir in the cheese until melted and smooth.
Add the drained pasta to the skillet and toss to combine with the sauce. Let it sit for a few minutes to thicken and allow the pasta to absorb the flavors.
Serve: Plate the pasta, garnish as desired, and serve immediately!