Bring a large pot of heavily salted water (approx. 2 tbsp salt) to a boil. You want it to be salty enough that it tastes like the ocean!
Once the water is boiling, add the orecchiette and let it cook for 3 minutes.
Add the broccoli florets to the pot and continue to boil for 8 minutes.
Using a glass measuring cup and holding the handle, ladle out ½ cup of the pasta water from the pot, set aside.
Using a strainer, drain the pasta and broccoli. Quickly return pasta and broccoli to the pot.
Add the minced garlic, butter and olive oil to the pasta and stir quickly until the butter is melted. Add in the reserved pasta water and continue to stir vigorously so that the broccoli breaks down in to a smooth consistency.
Add the grated parmesan and red pepper flakes, stir until thoroughly mixed in.