Bring a large pot of water to a boil, then season the water with 2-3 tablespoon of salt. Add the penne pasta and cook until al dente. Meanwhile, blanch the broccoli in water for 3-4 minutes, then strain and set aside.
In a frying pan, pour two tablespoons of olive oil, sauté the garlic until fragrant, approximately 3-4 minutes.
Add in the blanched broccoli to the sautéing garlic. Stir to combine and make sure the broccoli is fully coated. Add 2-3 more tablespoons of olive oil.
Once the pasta has finished cooking, add directly to the pan of broccoli, turn the flame onto a medium low and toss with the remaining two tablespoons of olive oil.
Notes
Make sure the pasta is al dente. Al dente translates to "to the tooth" which means that the pasta has a slight chew or resistance to it. When pasta is overcooked, it falls apart very quickly especially when tossed with other ingredients like broccoli. Cooking the pasta al dente helps to keep the shape and not break.You need to use wayyy more olive oil than you think. When I tested this the first few times years ago, I did not use nearly enough oil. I was nervous to use too much as I thought it would make it taste gross, but it does quite the opposite. The oil helps to soak and coat the broccoli, the garlic gives the oil flavor, and then as it simmers with the broccoli AND the pasta, it helps to evenly coat the broccoli and give flavor.Add salt throughout the cooking process. You want to salt the pasta water before adding in the pasta (1-2 tbsp), then add a pinch or two to the broccoli, then again as you add the broccoli to the garlic, and then another pinch or two (maybe three... I don't judge) to the dish when adding the pasta to the broccoli. Salt enhances the flavor of the dish, and adding another small pinch could make the difference.