Cook the Pasta: Bring a large pot of salted water to a steady boil. Add the orecchiette and cook until just tender, following the package timing. Stir occasionally so nothing sticks. Before draining, scoop out about one cup of pasta water and set it aside. Drain the pasta and keep it warm.
Blanch the Broccoli: While the pasta cooks, drop the broccoli florets into the same boiling water during the last two to three minutes. This keeps them bright and tender. Drain the broccoli with the pasta or scoop it out with a slotted spoon if you prefer firmer pieces.
Warm the Olive Oil: Place a wide pan over medium heat and pour in the olive oil. Let it heat gently until it shimmers. Avoid rushing this step since warm oil helps the garlic release flavor without burning.
Cook the Garlic: Add the minced garlic to the oil and stir constantly for about thirty seconds. The garlic should smell fragrant but stay pale. This step builds the base flavor for the entire dish.
Add Broccoli: Tip the broccoli into the pan with the garlic. Season with salt and pepper, then toss gently so the florets pick up the oil and garlic. Cook for two minutes until everything feels well combined.
Combine Pasta and Sauce: Add the cooked pasta to the pan along with a splash of reserved pasta water. Toss everything together so the starch from the water helps coat the pasta and broccoli evenly.
Finish with Cheese and Spice: Sprinkle in the Parmesan cheese and red pepper flakes. Stir gently until the cheese melts and forms a glossy coating. Add more pasta water if needed to loosen the sauce.
Taste and Adjust: Give the pasta a final taste. Add more salt, pepper, or cheese until it feels just right. Serve hot.
