Heat the oil over medium-low heat in a large frying pan fitted with a splatter screen and add the whole garlic cloves and the broccoli with a few dashes each of salt and pepper. Cook until the broccoli is fork tender, stirring often.
Meanwhile cook the pasta to al dente in plenty of salted water.
When the broccoli is tender remove the whole garlic cloves and discard them. Move the broccoli to the sides of the pan making a well in the middle.
Add the garlic and red pepper flakes to the well and stir until the garlic is fragrant about 2 minutes.
Add the drained pasta and toss well. Season to taste with salt and pepper and more red pepper flakes, if desired.
Serve with lots of grated Parm and another drizzle of olive oil, if needed.