In a large bowl, put the semolina flour and form a well in the centre. Add water and a pinch of salt to the well, then, with a fork, gradually incorporate the water until a dough is formed. Knead the dough, until smooth and elastic, for about 8 minutes. Wrap the dough in plastic wrap.
Dust your hands with some semolina flour. Remove 1 piece of dough from the plastic wrap and roll it to create a rope 1/2 inch wide. Put the rope on a work surface and with a knife cut into small pieces (big as a chickpea). Lightly toss cut pieces with a little semolina mixture. Shape the orecchiette.
Bring a medium saucepan filled with salted water to a boil over high heat. Blanch the broccoli by placing it in the boiling salted water for 2 minutes.
Drain the broccoli and leave to cool. Once cool, chop them into 1-inch pieces and set aside.
Cook pasta according to dimension and thickness.
While the pasta cooks, heat a large frying pan over medium heat. Add olive oil, garlic and red chilli flakes to taste. Cook for 1 minute.
Add drained and chopped broccoli and sauté until thoroughly heated and slightly wilted. Season it well with salt and freshly ground black pepper.
Before draining the pasta, remove a cup of pasta water and set it aside.
Add the drained pasta and toss it until it is coated with sauce. Adjust seasoning as necessary and serve.